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\n#include \"BigInt.hpp\"\n\nint main()\n{\n BigInt big1 = 1234567890, big2;\n big2 = \"987654321012345678909876543210123456789\";\n \n BigInt big3 = 1 + pow(2 * big1 + 3 * big2, 4);\n std::cout << big3 << \"\\n\";\n}\n","codes",[3346],{"_3347":3348,"_3342":3349},"file","BigInt.hpp","/*\n BigInt\n ------\n Arbitrary-sized integer class for C++.\n \n Version: 0.4.0-dev\n Released on: 03 January 2018 10:51 IST\n Author: Syed Faheel Ahmad (faheel@live.in)\n Project on GitHub: https://github.com/faheel/BigInt\n License: MIT\n*/\n\n/*\n ===========================================================================\n BigInt\n ===========================================================================\n Definition for the BigInt class.\n*/\n\n#ifndef BIG_INT_HPP\n#define BIG_INT_HPP\n\n#include \n\nclass BigInt {\n std::string value;\n char sign;\n\n public:\n // Constructors:\n BigInt();\n BigInt(const BigInt&);\n BigInt(const long long&);\n BigInt(const std::string&);\n\n // Assignment operators:\n BigInt& operator=(const BigInt&);\n BigInt& operator=(const long long&);\n BigInt& operator=(const std::string&);\n\n // Unary arithmetic operators:\n BigInt operator+() const; // unary +\n BigInt operator-() const; // unary -\n\n // Binary arithmetic operators:\n BigInt operator+(const BigInt&) const;\n BigInt operator-(const BigInt&) const;\n BigInt operator*(const BigInt&) const;\n BigInt operator/(const BigInt&) const;\n BigInt operator%(const BigInt&) const;\n BigInt operator+(const long long&) const;\n BigInt operator-(const long long&) const;\n BigInt operator*(const long long&) const;\n BigInt operator/(const long long&) const;\n BigInt operator%(const long long&) const;\n BigInt operator+(const std::string&) const;\n BigInt operator-(const std::string&) const;\n BigInt operator*(const std::string&) const;\n BigInt operator/(const std::string&) const;\n BigInt operator%(const std::string&) const;\n\n // Arithmetic-assignment operators:\n BigInt& operator+=(const BigInt&);\n BigInt& operator-=(const BigInt&);\n BigInt& operator*=(const BigInt&);\n BigInt& operator/=(const BigInt&);\n BigInt& operator%=(const BigInt&);\n BigInt& operator+=(const long long&);\n BigInt& operator-=(const long long&);\n BigInt& operator*=(const long long&);\n BigInt& operator/=(const long long&);\n BigInt& operator%=(const long long&);\n BigInt& operator+=(const std::string&);\n BigInt& operator-=(const std::string&);\n BigInt& operator*=(const std::string&);\n BigInt& operator/=(const std::string&);\n BigInt& operator%=(const std::string&);\n\n // Increment and decrement operators:\n BigInt& operator++(); // pre-increment\n BigInt& operator--(); // pre-decrement\n BigInt operator++(int); // post-increment\n BigInt operator--(int); // post-decrement\n\n // Relational operators:\n bool operator<(const BigInt&) const;\n bool operator>(const BigInt&) const;\n bool operator<=(const BigInt&) const;\n bool operator>=(const BigInt&) const;\n bool operator==(const BigInt&) const;\n bool operator!=(const BigInt&) const;\n bool operator<(const long long&) const;\n bool operator>(const long long&) const;\n bool operator<=(const long long&) const;\n bool operator>=(const long long&) const;\n bool operator==(const long long&) const;\n bool operator!=(const long long&) const;\n bool operator<(const std::string&) const;\n bool operator>(const std::string&) const;\n bool operator<=(const std::string&) const;\n bool operator>=(const std::string&) const;\n bool operator==(const std::string&) const;\n bool operator!=(const std::string&) const;\n\n // I/O stream operators:\n friend std::istream& operator>>(std::istream&, BigInt&);\n friend std::ostream& operator<<(std::ostream&, const BigInt&);\n\n // Conversion functions:\n std::string to_string() const;\n int to_int() const;\n long to_long() const;\n long long to_long_long() const;\n};\n\n#endif // BIG_INT_HPP\n\n\n/*\n ===========================================================================\n Utility functions\n ===========================================================================\n*/\n\n#ifndef BIG_INT_UTILITY_FUNCTIONS_HPP\n#define BIG_INT_UTILITY_FUNCTIONS_HPP\n\n#include \n\n\n/*\n is_valid_number\n ---------------\n Checks whether the given string is a valid integer.\n*/\n\nbool is_valid_number(const std::string& num) {\n for (char digit : num)\n if (digit < '0' or digit > '9')\n return false;\n\n return true;\n}\n\n\n/*\n strip_leading_zeroes\n --------------------\n Strip the leading zeroes from a number represented as a string.\n*/\n\nvoid strip_leading_zeroes(std::string& num) {\n size_t i;\n for (i = 0; i < num.size(); i++)\n if (num[i] != '0')\n break;\n\n if (i == num.size())\n num = \"0\";\n else\n num = num.substr(i);\n}\n\n\n/*\n add_leading_zeroes\n ------------------\n Adds a given number of leading zeroes to a string-represented integer `num`.\n*/\n\nvoid add_leading_zeroes(std::string& num, size_t num_zeroes) {\n num = std::string(num_zeroes, '0') + num;\n}\n\n\n/*\n add_trailing_zeroes\n -------------------\n Adds a given number of trailing zeroes to a string-represented integer `num`.\n*/\n\nvoid add_trailing_zeroes(std::string& num, size_t num_zeroes) {\n num += std::string(num_zeroes, '0');\n}\n\n\n/*\n get_larger_and_smaller\n ----------------------\n Identifies the given string-represented integers as `larger` and `smaller`,\n padding the smaller number with leading zeroes to make it equal in length to\n the larger number.\n*/\n\nstd::tuple get_larger_and_smaller(const std::string& num1,\n const std::string& num2) {\n std::string larger, smaller;\n if (num1.size() > num2.size() or\n (num1.size() == num2.size() and num1 > num2)) {\n larger = num1;\n smaller = num2;\n }\n else {\n larger = num2;\n smaller = num1;\n }\n\n // pad the smaller number with zeroes\n add_leading_zeroes(smaller, larger.size() - smaller.size());\n\n return std::make_tuple(larger, smaller);\n}\n\n#endif // BIG_INT_UTILITY_FUNCTIONS_HPP\n\n\n/*\n ===========================================================================\n Constructors\n ===========================================================================\n*/\n\n#ifndef BIG_INT_CONSTRUCTORS_HPP\n#define BIG_INT_CONSTRUCTORS_HPP\n\n\n\n/*\n Default constructor\n -------------------\n*/\n\nBigInt::BigInt() {\n value = \"0\";\n sign = '+';\n}\n\n\n/*\n Copy constructor\n ----------------\n*/\n\nBigInt::BigInt(const BigInt& num) {\n value = num.value;\n sign = num.sign;\n}\n\n\n/*\n Integer to BigInt\n -----------------\n*/\n\nBigInt::BigInt(const long long& num) {\n value = std::to_string(num);\n if (num < 0) {\n sign = '-';\n value = value.substr(1); // remove minus sign from value\n }\n else\n sign = '+';\n}\n\n\n/*\n String to BigInt\n ----------------\n*/\n\nBigInt::BigInt(const std::string& num) {\n if (num[0] == '+' or num[0] == '-') { // check for sign\n std::string magnitude = num.substr(1);\n if (is_valid_number(magnitude)) {\n value = magnitude;\n sign = num[0];\n }\n else {\n throw std::invalid_argument(\"Expected an integer, got \\'\" + num + \"\\'\");\n }\n }\n else { // if no sign is specified\n if (is_valid_number(num)) {\n value = num;\n sign = '+'; // positive by default\n }\n else {\n throw std::invalid_argument(\"Expected an integer, got \\'\" + num + \"\\'\");\n }\n }\n strip_leading_zeroes(value);\n}\n\n#endif // BIG_INT_CONSTRUCTORS_HPP\n\n\n/*\n ===========================================================================\n Conversion functions for BigInt\n ===========================================================================\n*/\n\n#ifndef BIG_INT_CONVERSION_FUNCTIONS_HPP\n#define BIG_INT_CONVERSION_FUNCTIONS_HPP\n\n\n/*\n to_string\n ---------\n Converts a BigInt to a string.\n*/\n\nstd::string BigInt::to_string() const {\n // prefix with sign if negative\n return this->sign == '-' ? \"-\" + this->value : this->value;\n}\n\n\n/*\n to_int\n ------\n Converts a BigInt to an int.\n NOTE: If the BigInt is out of range of an int, stoi() will throw an\n out_of_range exception.\n*/\n\nint BigInt::to_int() const {\n return std::stoi(this->to_string());\n}\n\n\n/*\n to_long\n -------\n Converts a BigInt to a long int.\n NOTE: If the BigInt is out of range of a long int, stol() will throw an\n out_of_range exception.\n*/\n\nlong BigInt::to_long() const {\n return std::stol(this->to_string());\n}\n\n\n/*\n to_long_long\n ------------\n Converts a BigInt to a long long int.\n NOTE: If the BigInt is out of range of a long long int, stoll() will throw\n an out_of_range exception.\n*/\n\nlong long BigInt::to_long_long() const {\n return std::stoll(this->to_string());\n}\n\n#endif // BIG_INT_CONVERSION_FUNCTIONS_HPP\n\n\n/*\n ===========================================================================\n Assignment operators\n ===========================================================================\n*/\n\n#ifndef BIG_INT_ASSIGNMENT_OPERATORS_HPP\n#define BIG_INT_ASSIGNMENT_OPERATORS_HPP\n\n\n\n/*\n BigInt = BigInt\n ---------------\n*/\n\nBigInt& BigInt::operator=(const BigInt& num) {\n value = num.value;\n sign = num.sign;\n\n return *this;\n}\n\n\n/*\n BigInt = Integer\n ----------------\n*/\n\nBigInt& BigInt::operator=(const long long& num) {\n BigInt temp(num);\n value = temp.value;\n sign = temp.sign;\n\n return *this;\n}\n\n\n/*\n BigInt = String\n ---------------\n*/\n\nBigInt& BigInt::operator=(const std::string& num) {\n BigInt temp(num);\n value = temp.value;\n sign = temp.sign;\n\n return *this;\n}\n\n#endif // BIG_INT_ASSIGNMENT_OPERATORS_HPP\n\n\n/*\n ===========================================================================\n Unary arithmetic operators\n ===========================================================================\n*/\n\n#ifndef BIG_INT_UNARY_ARITHMETIC_OPERATORS_HPP\n#define BIG_INT_UNARY_ARITHMETIC_OPERATORS_HPP\n\n\n\n/*\n +BigInt\n -------\n Returns the value of a BigInt.\n NOTE: This function does not return the absolute value. To get the absolute\n value of a BigInt, use the `abs` function.\n*/\n\nBigInt BigInt::operator+() const {\n return *this;\n}\n\n\n/*\n -BigInt\n -------\n Returns the negative of a BigInt.\n*/\n\nBigInt BigInt::operator-() const {\n BigInt temp;\n\n temp.value = value;\n if (value != \"0\") {\n if (sign == '+')\n temp.sign = '-';\n else\n temp.sign = '+';\n }\n\n return temp;\n}\n\n#endif // BIG_INT_UNARY_ARITHMETIC_OPERATORS_HPP\n\n\n/*\n ===========================================================================\n Relational operators\n ===========================================================================\n All operators depend on the '<' and/or '==' operator(s).\n*/\n\n#ifndef BIG_INT_RELATIONAL_OPERATORS_HPP\n#define BIG_INT_RELATIONAL_OPERATORS_HPP\n\n\n\n/*\n BigInt == BigInt\n ----------------\n*/\n\nbool BigInt::operator==(const BigInt& num) const {\n return (sign == num.sign) and (value == num.value);\n}\n\n\n/*\n BigInt != BigInt\n ----------------\n*/\n\nbool BigInt::operator!=(const BigInt& num) const {\n return !(*this == num);\n}\n\n\n/*\n BigInt < BigInt\n ---------------\n*/\n\nbool BigInt::operator<(const BigInt& num) const {\n if (sign == num.sign) {\n if (sign == '+') {\n if (value.length() == num.value.length())\n return value < num.value;\n else\n return value.length() < num.value.length();\n }\n else\n return -(*this) > -num;\n }\n else\n return sign == '-';\n}\n\n\n/*\n BigInt > BigInt\n ---------------\n*/\n\nbool BigInt::operator>(const BigInt& num) const {\n return !((*this < num) or (*this == num));\n}\n\n\n/*\n BigInt <= BigInt\n ----------------\n*/\n\nbool BigInt::operator<=(const BigInt& num) const {\n return (*this < num) or (*this == num);\n}\n\n\n/*\n BigInt >= BigInt\n ----------------\n*/\n\nbool BigInt::operator>=(const BigInt& num) const {\n return !(*this < num);\n}\n\n\n/*\n BigInt == Integer\n -----------------\n*/\n\nbool BigInt::operator==(const long long& num) const {\n return *this == BigInt(num);\n}\n\n\n/*\n Integer == BigInt\n -----------------\n*/\n\nbool operator==(const long long& lhs, const BigInt& rhs) {\n return BigInt(lhs) == rhs;\n}\n\n\n/*\n BigInt != Integer\n -----------------\n*/\n\nbool BigInt::operator!=(const long long& num) const {\n return !(*this == BigInt(num));\n}\n\n\n/*\n Integer != BigInt\n -----------------\n*/\n\nbool operator!=(const long long& lhs, const BigInt& rhs) {\n return BigInt(lhs) != rhs;\n}\n\n\n/*\n BigInt < Integer\n ----------------\n*/\n\nbool BigInt::operator<(const long long& num) const {\n return *this < BigInt(num);\n}\n\n\n/*\n Integer < BigInt\n ----------------\n*/\n\nbool operator<(const long long& lhs, const BigInt& rhs) {\n return BigInt(lhs) < rhs;\n}\n\n\n/*\n BigInt > Integer\n ----------------\n*/\n\nbool BigInt::operator>(const long long& num) const {\n return *this > BigInt(num);\n}\n\n\n/*\n Integer > BigInt\n ----------------\n*/\n\nbool operator>(const long long& lhs, const BigInt& rhs) {\n return BigInt(lhs) > rhs;\n}\n\n\n/*\n BigInt <= Integer\n -----------------\n*/\n\nbool BigInt::operator<=(const long long& num) const {\n return !(*this > BigInt(num));\n}\n\n\n/*\n Integer <= BigInt\n -----------------\n*/\n\nbool operator<=(const long long& lhs, const BigInt& rhs) {\n return BigInt(lhs) <= rhs;\n}\n\n\n/*\n BigInt >= Integer\n -----------------\n*/\n\nbool BigInt::operator>=(const long long& num) const {\n return !(*this < BigInt(num));\n}\n\n\n/*\n Integer >= BigInt\n -----------------\n*/\n\nbool operator>=(const long long& lhs, const BigInt& rhs) {\n return BigInt(lhs) >= rhs;\n}\n\n\n/*\n BigInt == String\n ----------------\n*/\n\nbool BigInt::operator==(const std::string& num) const {\n return *this == BigInt(num);\n}\n\n\n/*\n String == BigInt\n ----------------\n*/\n\nbool operator==(const std::string& lhs, const BigInt& rhs) {\n return BigInt(lhs) == rhs;\n}\n\n\n/*\n BigInt != String\n ----------------\n*/\n\nbool BigInt::operator!=(const std::string& num) const {\n return !(*this == BigInt(num));\n}\n\n\n/*\n String != BigInt\n ----------------\n*/\n\nbool operator!=(const std::string& lhs, const BigInt& rhs) {\n return BigInt(lhs) != rhs;\n}\n\n\n/*\n BigInt < String\n ---------------\n*/\n\nbool BigInt::operator<(const std::string& num) const {\n return *this < BigInt(num);\n}\n\n\n/*\n String < BigInt\n ---------------\n*/\n\nbool operator<(const std::string& lhs, const BigInt& rhs) {\n return BigInt(lhs) < rhs;\n}\n\n\n/*\n BigInt > String\n ---------------\n*/\n\nbool BigInt::operator>(const std::string& num) const {\n return *this > BigInt(num);\n}\n\n\n/*\n String > BigInt\n ---------------\n*/\n\nbool operator>(const std::string& lhs, const BigInt& rhs) {\n return BigInt(lhs) > rhs;\n}\n\n\n/*\n BigInt <= String\n ----------------\n*/\n\nbool BigInt::operator<=(const std::string& num) const {\n return !(*this > BigInt(num));\n}\n\n\n/*\n String <= BigInt\n ----------------\n*/\n\nbool operator<=(const std::string& lhs, const BigInt& rhs) {\n return BigInt(lhs) <= rhs;\n}\n\n\n/*\n BigInt >= String\n ----------------\n*/\n\nbool BigInt::operator>=(const std::string& num) const {\n return !(*this < BigInt(num));\n}\n\n\n/*\n String >= BigInt\n ----------------\n*/\n\nbool operator>=(const std::string& lhs, const BigInt& rhs) {\n return BigInt(lhs) >= rhs;\n}\n\n#endif // BIG_INT_RELATIONAL_OPERATORS_HPP\n\n\n/*\n ===========================================================================\n Math functions for BigInt\n ===========================================================================\n*/\n\n#ifndef BIG_INT_MATH_FUNCTIONS_HPP\n#define BIG_INT_MATH_FUNCTIONS_HPP\n\n#include \n\n\n\n/*\n abs\n ---\n Returns the absolute value of a BigInt.\n*/\n\nBigInt abs(const BigInt& num) {\n return num < 0 ? -num : num;\n}\n\n\n/*\n big_pow10\n ---------\n Returns a BigInt equal to 10^exp.\n NOTE: exponent should be a non-negative integer.\n*/\n\nBigInt big_pow10(size_t exp) {\n return BigInt(\"1\" + std::string(exp, '0'));\n}\n\n\n/*\n pow (BigInt)\n ------------\n Returns a BigInt equal to base^exp.\n*/\n\nBigInt pow(const BigInt& base, int exp) {\n if (exp < 0) {\n if (base == 0)\n throw std::logic_error(\"Cannot divide by zero\");\n return abs(base) == 1 ? base : 0;\n }\n if (exp == 0) {\n if (base == 0)\n throw std::logic_error(\"Zero cannot be raised to zero\");\n return 1;\n }\n\n BigInt result = base, result_odd = 1;\n while (exp > 1) {\n if (exp % 2)\n result_odd *= result;\n result *= result;\n exp /= 2;\n }\n\n return result * result_odd;\n}\n\n\n/*\n pow (Integer)\n -------------\n Returns a BigInt equal to base^exp.\n*/\n\nBigInt pow(const long long& base, int exp) {\n return pow(BigInt(base), exp);\n}\n\n\n/*\n pow (String)\n ------------\n Returns a BigInt equal to base^exp.\n*/\n\nBigInt pow(const std::string& base, int exp) {\n return pow(BigInt(base), exp);\n\n}\n\n\n/*\n sqrt\n ----\n Returns the positive integer square root of a BigInt using Newton's method.\n NOTE: the input must be non-negative.\n*/\n\nBigInt sqrt(const BigInt& num) {\n if (num < 0)\n throw std::invalid_argument(\"Cannot compute square root of a negative integer\");\n\n // Optimisations for small inputs:\n if (num == 0)\n return 0;\n else if (num < 4)\n return 1;\n else if (num < 9)\n return 2;\n else if (num < 16)\n return 3;\n\n BigInt sqrt_prev = 0;\n // The value for `sqrt_current` is chosen close to that of the actual\n // square root.\n // Since a number's square root has at least one less than half as many\n // digits as the number,\n // sqrt_current = 10^(half_the_digits_in_num - 1)\n BigInt sqrt_current = big_pow10(num.to_string().size() / 2 - 1);\n\n while (abs(sqrt_current - sqrt_prev) > 1) {\n sqrt_prev = sqrt_current;\n sqrt_current = (num / sqrt_prev + sqrt_prev) / 2;\n }\n\n return sqrt_current;\n}\n\n#endif // BIG_INT_MATH_FUNCTIONS_HPP\n\n\n/*\n ===========================================================================\n Binary arithmetic operators\n ===========================================================================\n*/\n\n#ifndef BIG_INT_BINARY_ARITHMETIC_OPERATORS_HPP\n#define BIG_INT_BINARY_ARITHMETIC_OPERATORS_HPP\n\n#include \n#include \n#include \n\n\nconst long long FLOOR_SQRT_LLONG_MAX = 3037000499;\n\n\n/*\n BigInt + BigInt\n ---------------\n The operand on the RHS of the addition is `num`.\n*/\n\nBigInt BigInt::operator+(const BigInt& num) const {\n // if the operands are of opposite signs, perform subtraction\n if (this->sign == '+' and num.sign == '-') {\n BigInt rhs = num;\n rhs.sign = '+';\n return *this - rhs;\n }\n else if (this->sign == '-' and num.sign == '+') {\n BigInt lhs = *this;\n lhs.sign = '+';\n return -(lhs - num);\n }\n\n // identify the numbers as `larger` and `smaller`\n std::string larger, smaller;\n std::tie(larger, smaller) = get_larger_and_smaller(this->value, num.value);\n\n BigInt result; // the resultant sum\n result.value = \"\"; // the value is cleared as the digits will be appended\n short carry = 0, sum;\n // add the two values\n for (long i = larger.size() - 1; i >= 0; i--) {\n sum = larger[i] - '0' + smaller[i] - '0' + carry;\n result.value = std::to_string(sum % 10) + result.value;\n carry = sum / (short) 10;\n }\n if (carry)\n result.value = std::to_string(carry) + result.value;\n\n // if the operands are negative, the result is negative\n if (this->sign == '-' and result.value != \"0\")\n result.sign = '-';\n\n return result;\n}\n\n\n/*\n BigInt - BigInt\n ---------------\n The operand on the RHS of the subtraction is `num`.\n*/\n\nBigInt BigInt::operator-(const BigInt& num) const {\n // if the operands are of opposite signs, perform addition\n if (this->sign == '+' and num.sign == '-') {\n BigInt rhs = num;\n rhs.sign = '+';\n return *this + rhs;\n }\n else if (this->sign == '-' and num.sign == '+') {\n BigInt lhs = *this;\n lhs.sign = '+';\n return -(lhs + num);\n }\n\n BigInt result; // the resultant difference\n // identify the numbers as `larger` and `smaller`\n std::string larger, smaller;\n if (abs(*this) > abs(num)) {\n larger = this->value;\n smaller = num.value;\n\n if (this->sign == '-') // -larger - -smaller = -result\n result.sign = '-';\n }\n else {\n larger = num.value;\n smaller = this->value;\n\n if (num.sign == '+') // smaller - larger = -result\n result.sign = '-';\n }\n // pad the smaller number with zeroes\n add_leading_zeroes(smaller, larger.size() - smaller.size());\n\n result.value = \"\"; // the value is cleared as the digits will be appended\n short difference;\n long i, j;\n // subtract the two values\n for (i = larger.size() - 1; i >= 0; i--) {\n difference = larger[i] - smaller[i];\n if (difference < 0) {\n for (j = i - 1; j >= 0; j--) {\n if (larger[j] != '0') {\n larger[j]--; // borrow from the j-th digit\n break;\n }\n }\n j++;\n while (j != i) {\n larger[j] = '9'; // add the borrow and take away 1\n j++;\n }\n difference += 10; // add the borrow\n }\n result.value = std::to_string(difference) + result.value;\n }\n strip_leading_zeroes(result.value);\n\n // if the result is 0, set its sign as +\n if (result.value == \"0\")\n result.sign = '+';\n\n return result;\n}\n\n\n/*\n BigInt * BigInt\n ---------------\n Computes the product of two BigInts using Karatsuba's algorithm.\n The operand on the RHS of the product is `num`.\n*/\n\nBigInt BigInt::operator*(const BigInt& num) const {\n if (*this == 0 or num == 0)\n return BigInt(0);\n if (*this == 1)\n return num;\n if (num == 1)\n return *this;\n\n BigInt product;\n if (abs(*this) <= FLOOR_SQRT_LLONG_MAX and abs(num) <= FLOOR_SQRT_LLONG_MAX)\n product = std::stoll(this->value) * std::stoll(num.value);\n else {\n // identify the numbers as `larger` and `smaller`\n std::string larger, smaller;\n std::tie(larger, smaller) = get_larger_and_smaller(this->value, num.value);\n\n size_t half_length = larger.size() / 2;\n auto half_length_ceil = (size_t) ceil(larger.size() / 2.0);\n\n BigInt num1_high, num1_low;\n num1_high = larger.substr(0, half_length);\n num1_low = larger.substr(half_length);\n\n BigInt num2_high, num2_low;\n num2_high = smaller.substr(0, half_length);\n num2_low = smaller.substr(half_length);\n\n strip_leading_zeroes(num1_high.value);\n strip_leading_zeroes(num1_low.value);\n strip_leading_zeroes(num2_high.value);\n strip_leading_zeroes(num2_low.value);\n\n BigInt prod_high, prod_mid, prod_low;\n prod_high = num1_high * num2_high;\n prod_low = num1_low * num2_low;\n prod_mid = (num1_high + num1_low) * (num2_high + num2_low)\n - prod_high - prod_low;\n\n add_trailing_zeroes(prod_high.value, 2 * half_length_ceil);\n add_trailing_zeroes(prod_mid.value, half_length_ceil);\n\n strip_leading_zeroes(prod_high.value);\n strip_leading_zeroes(prod_mid.value);\n strip_leading_zeroes(prod_low.value);\n\n product = prod_high + prod_mid + prod_low;\n }\n strip_leading_zeroes(product.value);\n\n if (this->sign == num.sign)\n product.sign = '+';\n else\n product.sign = '-';\n\n return product;\n}\n\n\n/*\n divide\n ------\n Helper function that returns the quotient and remainder on dividing the\n dividend by the divisor, when the divisor is 1 to 10 times the dividend.\n*/\n\nstd::tuple divide(const BigInt& dividend, const BigInt& divisor) {\n BigInt quotient, remainder, temp;\n\n temp = divisor;\n quotient = 1;\n while (temp < dividend) {\n quotient++;\n temp += divisor;\n }\n if (temp > dividend) {\n quotient--;\n remainder = dividend - (temp - divisor);\n }\n\n return std::make_tuple(quotient, remainder);\n}\n\n\n/*\n BigInt / BigInt\n ---------------\n Computes the quotient of two BigInts using the long-division method.\n The operand on the RHS of the division (the divisor) is `num`.\n*/\n\nBigInt BigInt::operator/(const BigInt& num) const {\n BigInt abs_dividend = abs(*this);\n BigInt abs_divisor = abs(num);\n\n if (num == 0)\n throw std::logic_error(\"Attempted division by zero\");\n if (abs_dividend < abs_divisor)\n return BigInt(0);\n if (num == 1)\n return *this;\n if (num == -1)\n return -(*this);\n\n BigInt quotient;\n if (abs_dividend <= LLONG_MAX and abs_divisor <= LLONG_MAX)\n quotient = std::stoll(abs_dividend.value) / std::stoll(abs_divisor.value);\n else if (abs_dividend == abs_divisor)\n quotient = 1;\n else {\n quotient.value = \"\"; // the value is cleared as digits will be appended\n BigInt chunk, chunk_quotient, chunk_remainder;\n size_t chunk_index = 0;\n chunk_remainder.value = abs_dividend.value.substr(chunk_index, abs_divisor.value.size() - 1);\n chunk_index = abs_divisor.value.size() - 1;\n while (chunk_index < abs_dividend.value.size()) {\n chunk.value = chunk_remainder.value.append(1, abs_dividend.value[chunk_index]);\n chunk_index++;\n while (chunk < abs_divisor) {\n quotient.value += \"0\";\n if (chunk_index < abs_dividend.value.size()) {\n chunk.value.append(1, abs_dividend.value[chunk_index]);\n chunk_index++;\n }\n else\n break;\n }\n if (chunk == abs_divisor) {\n quotient.value += \"1\";\n chunk_remainder = 0;\n }\n else if (chunk > abs_divisor) {\n strip_leading_zeroes(chunk.value);\n std::tie(chunk_quotient, chunk_remainder) = divide(chunk, abs_divisor);\n quotient.value += chunk_quotient.value;\n }\n }\n }\n strip_leading_zeroes(quotient.value);\n\n if (this->sign == num.sign)\n quotient.sign = '+';\n else\n quotient.sign = '-';\n\n return quotient;\n}\n\n\n/*\n BigInt % BigInt\n ---------------\n Computes the modulo (remainder on division) of two BigInts.\n The operand on the RHS of the modulo (the divisor) is `num`.\n*/\n\nBigInt BigInt::operator%(const BigInt& num) const {\n BigInt abs_dividend = abs(*this);\n BigInt abs_divisor = abs(num);\n\n if (abs_divisor == 0)\n throw std::logic_error(\"Attempted division by zero\");\n if (abs_divisor == 1 or abs_divisor == abs_dividend)\n return BigInt(0);\n\n BigInt remainder;\n if (abs_dividend <= LLONG_MAX and abs_divisor <= LLONG_MAX)\n remainder = std::stoll(abs_dividend.value) % std::stoll(abs_divisor.value);\n else if (abs_dividend < abs_divisor)\n remainder = abs_dividend;\n else {\n BigInt quotient = abs_dividend / abs_divisor;\n remainder = abs_dividend - quotient * abs_divisor;\n }\n strip_leading_zeroes(remainder.value);\n\n // remainder has the same sign as that of the dividend\n remainder.sign = this->sign;\n if (remainder.value == \"0\") // except if its zero\n remainder.sign = '+';\n\n return remainder;\n}\n\n\n/*\n BigInt + Integer\n ----------------\n*/\n\nBigInt BigInt::operator+(const long long& num) const {\n return *this + BigInt(num);\n}\n\n\n/*\n Integer + BigInt\n ----------------\n*/\n\nBigInt operator+(const long long& lhs, const BigInt& rhs) {\n return BigInt(lhs) + rhs;\n}\n\n\n/*\n BigInt - Integer\n ----------------\n*/\n\nBigInt BigInt::operator-(const long long& num) const {\n return *this - BigInt(num);\n}\n\n\n/*\n Integer - BigInt\n ----------------\n*/\n\nBigInt operator-(const long long& lhs, const BigInt& rhs) {\n return BigInt(lhs) - rhs;\n}\n\n\n/*\n BigInt * Integer\n ----------------\n*/\n\nBigInt BigInt::operator*(const long long& num) const {\n return *this * BigInt(num);\n}\n\n\n/*\n Integer * BigInt\n ----------------\n*/\n\nBigInt operator*(const long long& lhs, const BigInt& rhs) {\n return BigInt(lhs) * rhs;\n}\n\n\n/*\n BigInt / Integer\n ----------------\n*/\n\nBigInt BigInt::operator/(const long long& num) const {\n return *this / BigInt(num);\n}\n\n\n/*\n Integer / BigInt\n ----------------\n*/\n\nBigInt operator/(const long long& lhs, const BigInt& rhs) {\n return BigInt(lhs) / rhs;\n}\n\n\n/*\n BigInt % Integer\n ----------------\n*/\n\nBigInt BigInt::operator%(const long long& num) const {\n return *this % BigInt(num);\n}\n\n\n/*\n Integer % BigInt\n ----------------\n*/\n\nBigInt operator%(const long long& lhs, const BigInt& rhs) {\n return BigInt(lhs) % rhs;\n}\n\n\n/*\n BigInt + String\n ---------------\n*/\n\nBigInt BigInt::operator+(const std::string& num) const {\n return *this + BigInt(num);\n}\n\n\n/*\n String + BigInt\n ---------------\n*/\n\nBigInt operator+(const std::string& lhs, const BigInt& rhs) {\n return BigInt(lhs) + rhs;\n}\n\n\n/*\n BigInt - String\n ---------------\n*/\n\nBigInt BigInt::operator-(const std::string& num) const {\n return *this - BigInt(num);\n}\n\n\n/*\n String - BigInt\n ---------------\n*/\n\nBigInt operator-(const std::string& lhs, const BigInt& rhs) {\n return BigInt(lhs) - rhs;\n}\n\n\n/*\n BigInt * String\n ---------------\n*/\n\nBigInt BigInt::operator*(const std::string& num) const {\n return *this * BigInt(num);\n}\n\n\n/*\n String * BigInt\n ---------------\n*/\n\nBigInt operator*(const std::string& lhs, const BigInt& rhs) {\n return BigInt(lhs) * rhs;\n}\n\n\n/*\n BigInt / String\n ---------------\n*/\n\nBigInt BigInt::operator/(const std::string& num) const {\n return *this / BigInt(num);\n}\n\n\n/*\n String / BigInt\n ---------------\n*/\n\nBigInt operator/(const std::string& lhs, const BigInt& rhs) {\n return BigInt(lhs) / rhs;\n}\n\n\n/*\n BigInt % String\n ---------------\n*/\n\nBigInt BigInt::operator%(const std::string& num) const {\n return *this % BigInt(num);\n}\n\n\n/*\n String % BigInt\n ---------------\n*/\n\nBigInt operator%(const std::string& lhs, const BigInt& rhs) {\n return BigInt(lhs) % rhs;\n}\n\n#endif // BIG_INT_BINARY_ARITHMETIC_OPERATORS_HPP\n\n\n/*\n ===========================================================================\n Arithmetic-assignment operators\n ===========================================================================\n*/\n\n#ifndef BIG_INT_ARITHMETIC_ASSIGNMENT_OPERATORS_HPP\n#define BIG_INT_ARITHMETIC_ASSIGNMENT_OPERATORS_HPP\n\n\n\n/*\n BigInt += BigInt\n ----------------\n*/\n\nBigInt& BigInt::operator+=(const BigInt& num) {\n *this = *this + num;\n\n return *this;\n}\n\n\n/*\n BigInt -= BigInt\n ----------------\n*/\n\nBigInt& BigInt::operator-=(const BigInt& num) {\n *this = *this - num;\n\n return *this;\n}\n\n\n/*\n BigInt *= BigInt\n ----------------\n*/\n\nBigInt& BigInt::operator*=(const BigInt& num) {\n *this = *this * num;\n\n return *this;\n}\n\n\n/*\n BigInt /= BigInt\n ----------------\n*/\n\nBigInt& BigInt::operator/=(const BigInt& num) {\n *this = *this / num;\n\n return *this;\n}\n\n\n/*\n BigInt %= BigInt\n ----------------\n*/\n\nBigInt& BigInt::operator%=(const BigInt& num) {\n *this = *this % num;\n\n return *this;\n}\n\n\n/*\n BigInt += Integer\n -----------------\n*/\n\nBigInt& BigInt::operator+=(const long long& num) {\n *this = *this + BigInt(num);\n\n return *this;\n}\n\n\n/*\n BigInt -= Integer\n -----------------\n*/\n\nBigInt& BigInt::operator-=(const long long& num) {\n *this = *this - BigInt(num);\n\n return *this;\n}\n\n\n/*\n BigInt *= Integer\n -----------------\n*/\n\nBigInt& BigInt::operator*=(const long long& num) {\n *this = *this * BigInt(num);\n\n return *this;\n}\n\n\n/*\n BigInt /= Integer\n -----------------\n*/\n\nBigInt& BigInt::operator/=(const long long& num) {\n *this = *this / BigInt(num);\n\n return *this;\n}\n\n\n/*\n BigInt %= Integer\n -----------------\n*/\n\nBigInt& BigInt::operator%=(const long long& num) {\n *this = *this % BigInt(num);\n\n return *this;\n}\n\n\n/*\n BigInt += String\n ----------------\n*/\n\nBigInt& BigInt::operator+=(const std::string& num) {\n *this = *this + BigInt(num);\n\n return *this;\n}\n\n\n/*\n BigInt -= String\n ----------------\n*/\n\nBigInt& BigInt::operator-=(const std::string& num) {\n *this = *this - BigInt(num);\n\n return *this;\n}\n\n\n/*\n BigInt *= String\n ----------------\n*/\n\nBigInt& BigInt::operator*=(const std::string& num) {\n *this = *this * BigInt(num);\n\n return *this;\n}\n\n\n/*\n BigInt /= String\n ----------------\n*/\n\nBigInt& BigInt::operator/=(const std::string& num) {\n *this = *this / BigInt(num);\n\n return *this;\n}\n\n\n/*\n BigInt %= String\n ----------------\n*/\n\nBigInt& BigInt::operator%=(const std::string& num) {\n *this = *this % BigInt(num);\n\n return *this;\n}\n\n#endif // BIG_INT_ARITHMETIC_ASSIGNMENT_OPERATORS_HPP\n\n\n/*\n ===========================================================================\n Increment and decrement operators\n ===========================================================================\n*/\n\n#ifndef BIG_INT_INCREMENT_DECREMENT_OPERATORS_HPP\n#define BIG_INT_INCREMENT_DECREMENT_OPERATORS_HPP\n\n\n\n/*\n Pre-increment\n -------------\n ++BigInt\n*/\n\nBigInt& BigInt::operator++() {\n *this += 1;\n\n return *this;\n}\n\n\n/*\n Pre-decrement\n -------------\n --BigInt\n*/\n\nBigInt& BigInt::operator--() {\n *this -= 1;\n\n return *this;\n}\n\n\n/*\n Post-increment\n --------------\n BigInt++\n*/\n\nBigInt BigInt::operator++(int) {\n BigInt temp = *this;\n *this += 1;\n\n return temp;\n}\n\n\n/*\n Post-decrement\n --------------\n BigInt--\n*/\n\nBigInt BigInt::operator--(int) {\n BigInt temp = *this;\n *this -= 1;\n\n return temp;\n}\n\n#endif // BIG_INT_INCREMENT_DECREMENT_OPERATORS_HPP\n\n\n/*\n ===========================================================================\n I/O stream operators\n ===========================================================================\n*/\n\n#ifndef BIG_INT_IO_STREAM_OPERATORS_HPP\n#define BIG_INT_IO_STREAM_OPERATORS_HPP\n\n\n\n/*\n BigInt from input stream\n ------------------------\n*/\n\nstd::istream& operator>>(std::istream& in, BigInt& num) {\n std::string input;\n in >> input;\n num = BigInt(input); // remove sign from value and set sign, if exists\n\n return in;\n}\n\n\n/*\n BigInt to output stream\n -----------------------\n*/\n\nstd::ostream& operator<<(std::ostream& out, const BigInt& num) {\n if (num.sign == '-')\n out << num.sign;\n out << num.value;\n\n return out;\n}\n\n#endif // 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