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\n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\n\nusing namespace std;\n\nconst uint64_t BASE_POWER = 9;\n\ntypedef long double ldouble;\ntypedef complex Complex;\n\nconst ldouble PI = acosl(-1);\n\n\nuint64_t next_pow2(uint64_t value, unsigned maxb = sizeof(uint64_t) * CHAR_BIT, unsigned curb = 1) {\n\treturn maxb <= curb ? value : next_pow2(((value - 1) | ((value - 1) >> curb)) + 1, maxb, curb << 1);\n}\n\nuint64_t lg(uint64_t n) {\n\treturn n == 1 ? 0 : 1 + lg(n >> 1);\n}\n\nuint64_t sqr(uint64_t a) {\n\treturn a * a;\n}\n\nuint64_t power(uint64_t a, uint64_t n) {\n\treturn n == 0 ? 1 : sqr(power(a, n / 2)) * (n % 2 == 0 ? 1 : a);\n}\n\nvalarray pow(valarray a, int64_t power_) {\n\ttransform(begin(a), end(a), begin(a), [power_](Complex base) { return pow(base, power_); });\n\treturn a;\n}\n\nuint64_t random(uint64_t a = 0, uint64_t b = numeric_limits::max()) {\n auto tmp = mt19937(random_device()());\n\treturn uniform_int_distribution(a, b)(tmp);\n}\nclass LNumHasher;\n\nclass LNum {\n\tvector parts;\n\tconst uint64_t base = std::pow(10, BASE_POWER);\n\tuint64_t N, P;\n#if _DEBUG\n\tstring repr;\n#endif\npublic:\n\tLNum(string str) {\n\t\twhile (str.length() >= BASE_POWER) {\n\t\t\tparts.push_back(stoull(str.substr(str.length() - BASE_POWER, BASE_POWER)));\n\t\t\tstr.erase(str.length() - BASE_POWER, BASE_POWER);\n\t\t}\n\t\tif (str.length() > 0) {\n\t\t\tparts.push_back(stoull(str.substr(0, str.length())));\n\t\t}\n#if _DEBUG\n\t\trepr = to_str();\n#endif\n\t}\n\n\tLNum(uint64_t i) : LNum(to_string(i)) {}\n\n\tLNum(vector parts) : parts(parts) {\n#if _DEBUG\n\t\trepr = to_str();\n#endif\n\t}\n\n\tuint64_t bits() {\n\t\tLNum var = *this;\n\t\tuint64_t bits;\n\t\tfor (bits = 0; var != 0; ++bits) var /= 2;\n\t\treturn bits;\n\t}\n\n\tLNum& operator =(LNum other) {\n\t\tif (&other == this)\n\t\t\treturn *this;\n\t\tparts = other.parts;\n#if _DEBUG\n\t\trepr = to_str();\n#endif\n\t\treturn *this;\n\t}\n\n\tLNum(const LNum& other) {\n\t\tparts = other.parts;\n#if _DEBUG\n\t\trepr = to_str();\n#endif\n\t}\n\n\tstatic LNum random(LNum from, LNum to) {\n\t\tLNum diff = to - from;\n\t\tvector parts(diff.parts.size());\n\t\tfor_each(parts.begin(), prev(parts.end()), [](uint64_t& p) {\n\t\t\tp = ::random(0, base_max());\n\t\t\t});\n\t\tuint8_t carry = parts.size() > 1 ? LNum(vector(diff.parts.begin(), prev(diff.parts.end()))) < LNum(vector(parts.begin(), prev(parts.end()))) : 0;\n\t\tparts[parts.size() - 1] = ::random(0, diff.parts[parts.size() - 1] - carry);\n\t\tremove_zeros(parts);\n\t\treturn from + LNum(parts);\n\t}\n\n\tLNum& operator +=(const LNum& rhs) {\n\t\t*this = *this + rhs;\n\t\treturn *this;\n\t}\n\n\tLNum operator+(const LNum& rhs) const {\n\t\tLNum lhs = *this;\n\t\tuint64_t carry = 0;\n\t\tfor (size_t i = 0; i < max(lhs.parts.size(), rhs.parts.size()) || carry; ++i) {\n\t\t\tif (i == lhs.parts.size())\n\t\t\t\tlhs.parts.push_back(0);\n\t\t\tlhs.parts[i] += carry + (i < rhs.parts.size() ? rhs.parts[i] : 0);\n\t\t\tcarry = lhs.parts[i] >= base;\n\t\t\tif (carry) lhs.parts[i] -= base;\n\t\t}\n\t\treturn lhs;\n\t}\n\n\tstatic LNum plus_mod(const LNum& rhs, const LNum& lhs, uint64_t mod) {\n\t\treturn ((rhs % mod) + (lhs % mod)) % mod;\n\t}\n\tstatic LNum minus_mod(const LNum& rhs, const LNum& lhs, uint64_t mod) {\n\t\treturn ((rhs % mod) - (lhs % mod)) % mod;\n\t}\n\tstatic LNum mul_mod(const LNum& rhs, const LNum& lhs, uint64_t mod) {\n\t\treturn ((rhs % mod) * (lhs % mod)) % mod;\n\t}\n\tstatic LNum div_mod(const LNum& rhs, const LNum& lhs, uint64_t mod) {\n\t\treturn ((rhs % mod) / (lhs % mod)) % mod;\n\t}\n\tstatic LNum mod_mod(const LNum& rhs, const LNum& lhs, uint64_t mod) {\n\t\treturn ((rhs % mod) % (lhs % mod)) % mod;\n\t}\n\tLNum pow_mod(LNum exp, LNum modulus) {\n\t\tLNum base = *this;\n\t\tbase = base % modulus;\n\t\tLNum result = 1;\n\t\twhile (exp > 0) {\n\t\t\tif ((exp % 2) == 1) {\n\t\t\t\tresult = (result * base) % modulus;\n\t\t\t}\n\n\t\t\tbase = (base * base) % modulus;\n\t\t\texp = exp / 2;\n\t\t}\n\t\treturn result;\n\t}\n\n\tLNum& operator -=(const LNum& rhs) {\n\t\t*this = *this - rhs;\n\t\treturn *this;\n\t}\n\n\tLNum operator-(const LNum& rhs) const {\n#if _DEBUG\n\t\tassert(LNum(*this) >= rhs);\n#endif\n\t\tLNum lhs = *this;\n\t\tuint64_t carry = 0;\n\t\tfor (size_t i = 0; i < rhs.parts.size() || carry; ++i) {\n\t\t\tuint64_t temp = carry + (i < rhs.parts.size() ? rhs.parts[i] : 0);\n\t\t\tcarry = lhs.parts[i] < temp;\n\t\t\tif (carry) {\n#if _DEBUG\n\t\t\t\tassert(base > temp);\n#endif\n\t\t\t\tlhs.parts[i] += base - temp;\n\t\t\t}\n\t\t\telse {\n\t\t\t\tlhs.parts[i] -= temp;\n\t\t\t}\n\n\t\t}\n\t\tremove_zeros(lhs.parts);\n\n\t\treturn lhs;\n\t}\n\n\tLNum& operator /=(const LNum& rhs) {\n\t\t*this = *this / rhs;\n\t\treturn *this;\n\t}\n\n\tLNum operator /(const LNum& rhs) const {\n\t\tLNum lhs = *this;\n\t\tLNum res = 0;\n\t\tres.parts.resize(lhs.parts.size());\n\t\tLNum curValue = 0;\n\t\tfor (int64_t i = lhs.parts.size() - 1; i >= 0; i--) {\n\t\t\tcurValue = curValue * base;\n\n\t\t\tcurValue.parts[0] = lhs.parts[i];\n\t\t\t// подбираем максимальное число x, такое что b * x <= curValue\n\t\t\tint64_t x = 0;\n\t\t\tint64_t l = 0, r = base;\n\t\t\twhile (l <= r) {\n\t\t\t\tint64_t m = (l + r) >> 1;\n\t\t\t\tLNum cur = rhs * m;\n\t\t\t\tif (cur <= curValue) {\n\t\t\t\t\tx = m;\n\t\t\t\t\tl = m + 1;\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tr = m - 1;\n\t\t\t\t}\n\t\t\t}\n\t\t\tres.parts[i] = x;\n\t\t\tcurValue = curValue - rhs * LNum(x);\n\t\t}\n\n\t\tremove_zeros(res.parts);\n\t\treturn res;\n\t}\n\n\tLNum& operator %=(const LNum& rhs) {\n\t\t*this = *this % rhs;\n\t\treturn *this;\n\t}\n\n\tLNum operator %(const LNum& rhs) const {\n\t\tLNum lhs = *this;\n\t\tLNum res = 0;\n\t\tres.parts.resize(lhs.parts.size());\n\t\tLNum curValue = 0;\n\t\tfor (ptrdiff_t i = lhs.parts.size() - 1; i >= 0; i--) {\n\t\t\tcurValue = curValue * base;\n\n\t\t\tcurValue.parts[0] = lhs.parts[i];\n\t\t\t// подбираем максимальное число x, такое что b * x <= curValue\n\t\t\tint64_t x = 0;\n\t\t\tint64_t l = 0, r = base;\n\t\t\twhile (l <= r) {\n\t\t\t\tint64_t m = (l + r) >> 1;\n\t\t\t\tLNum cur = rhs * m;\n\t\t\t\tif (cur <= curValue)\n\t\t\t\t{\n\t\t\t\t\tx = m;\n\t\t\t\t\tl = m + 1;\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tr = m - 1;\n\t\t\t\t}\n\t\t\t}\n\t\t\tres.parts[i] = x;\n\t\t\tcurValue -= rhs * LNum(x);\n\t\t}\n\n\t\treturn curValue;\n\t}\n\n\tLNum& operator %=(const uint64_t& rhs) {\n\t\t*this = *this % rhs;\n\t\treturn *this;\n\t}\n\n\tint64_t operator %(const uint64_t& rhs) const {\n\t\tLNum lhs = *this;\n\t\tint64_t carry = 0;\n\t\tfor (int64_t i = (int64_t)lhs.parts.size() - 1; i >= 0; --i) {\n\t\t\tint64_t cur = lhs.parts[i] + carry * 1ll * base;\n\t\t\tlhs.parts[i] = int64_t(cur / rhs);\n\t\t\tcarry = int64_t(cur % rhs);\n\t\t}\n\t\treturn carry;\n\t}\n\n\tLNum& operator *=(const LNum& rhs) {\n\t\t*this = *this * rhs;\n\t\treturn *this;\n\t}\n\n\tLNum operator *(const LNum& rhs) const {\n\t\tLNum lhs = *this;\n\t\tvector c((lhs.parts.size() + rhs.parts.size()) * 2);\n\t\tfor (size_t i = 0; i < lhs.parts.size(); ++i)\n\t\t\tfor (size_t j = 0, carry = 0; j < rhs.parts.size() || carry; ++j) {\n\t\t\t\tuint64_t cur = c[i + j] + lhs.parts[i] * 1ll * (j < (uint64_t)rhs.parts.size() ? rhs.parts[j] : 0) + carry;\n\t\t\t\tc[i + j] = uint64_t(cur % base);\n\t\t\t\tcarry = uint64_t(cur / base);\n\t\t\t}\n\t\tremove_zeros(c);\n\t\tlhs.parts = c;\n\t\treturn lhs;\n\t}\n\n\tLNum& operator *=(const uint64_t& rhs) {\n\t\t*this = *this * rhs;\n\t\treturn *this;\n\t}\n\n\tLNum operator *(const uint64_t& rhs) const {\n\t\tLNum lhs = *this;\n\t\tuint64_t carry = 0;\n\t\tfor (size_t i = 0; i < lhs.parts.size() || carry; ++i) {\n\t\t\tif (i == lhs.parts.size())\n\t\t\t\tlhs.parts.push_back(0);\n\t\t\tuint64_t cur = carry + lhs.parts[i] * 1ll * rhs;\n\t\t\tlhs.parts[i] = uint64_t(cur % base);\n\t\t\tcarry = uint64_t(cur / base);\n\t\t}\n\t\tremove_zeros(lhs.parts);\n\t\treturn lhs;\n\t}\n\n\tLNum& operator ^=(const LNum& rhs) {\n\t\t*this = *this ^ rhs;\n\t\treturn *this;\n\t}\n\n\tLNum operator ^(const LNum& rhs) const {\n\t\tLNum res = 1;\n\t\tLNum cur = *this;\n\t\tLNum temp = rhs;\n\t\twhile (temp != 0) {\n\t\t\tif (temp % 2 == 1)\n\t\t\t\tres *= cur;\n\t\t\tcur *= cur;\n\t\t\ttemp /= 2;\n\t\t}\n\t\treturn res;\n\t}\n\n\tvalarray ComputeZeta() {\n\t\tvalarray zeta(P);\n\t\tfor (uint64_t k = 0; k < P; ++k) {\n\t\t\tzeta[k] = exp(1il * PI * ldouble(2 * k + 1) / ldouble(N));\n\t\t}\n\t\treturn zeta;\n\t}\n\n\tLNum& mulFur(LNum rhs) {\n\t\tconst uint64_t n = next_pow2(this->bits() + rhs.bits());\n\t\tP = next_pow2(log2(n));\n\t\tN = 2 * n / std::pow(P, 2);\n\n\t\tauto x = exp(1il * PI / ldouble(P)) * exp(1il * PI / ldouble(P));\n\n\t\tvalarray dzeta = ComputeZeta();\n\n\t\tauto a = half_fft(decompose(*this), dzeta);\n\t\tauto a1 = compose(inv_half_fft(a, dzeta)).to_str();\n\t\tauto b = half_fft(decompose(rhs), dzeta);\n\t\tauto b1 = compose(inv_half_fft(b, dzeta)).to_str();\n\n\t\tvector> c(N);\n\t\tfor (size_t i = 0; i < N; ++i) {\n\t\t\t//c[i].resize(P);\n\t\t\t//valarray f1(P);\n\t\t\t//valarray f2(P);\n\t\t\t//for (uint64_t j = 0; j < P; ++j) {\n\t\t\t//\tf1[j] = (a[i][j].real() * b[i][j].real() - a[i][j].imag() * b[i][j].imag()); //% (std::pow(2, n) + 1);\n\t\t\t//\tf2[j] = (a[i][j].real() * b[i][j].imag() + a[i][j].imag() * b[i][j].real());// % (std::pow(2, n) + 1);\n\t\t\t//}\n\t\t\t//transform(begin(f1), end(f1), begin(f2), begin(c[i]), [](ldouble da, ldouble db) {\n\t\t\t//\treturn Complex(da, db);\n\t\t\t//});\n\t\t\tc[i] = a[i] * b[i];\n\t\t}\n\n\t\t*this = compose(inv_half_fft(c, dzeta));\n\t\treturn *this;\n\t}\n\n\tstatic LNum mulFur(LNum lhs, LNum rhs)\n\t{\n\t\treturn lhs.mulFur(rhs);\n\t}\n\n\tbool operator <(const LNum& rhs) {\n\t\tif (parts.size() != rhs.parts.size())\n\t\t\treturn parts.size() < rhs.parts.size();\n\t\tfor (int64_t i = parts.size() - 1; i >= 0; --i)\n\t\t\tif (parts[i] != rhs.parts[i])\n\t\t\t\treturn parts[i] < rhs.parts[i];\n\t\treturn false;\n\t}\n\n\tbool operator >(const LNum& rhs) {\n\t\treturn !(*this <= rhs);\n\t}\n\n\tbool operator <=(const LNum& rhs) {\n\t\treturn *this < rhs || *this == rhs;\n\t}\n\n\tbool operator >=(const LNum& rhs) {\n\t\treturn !(*this < rhs);\n\t}\n\n\tbool operator == (const LNum& rhs) const {\n\t\tif (parts.size() != rhs.parts.size())\n\t\t\treturn false;\n\t\tfor (int64_t i = parts.size() - 1; i >= 0; --i)\n\t\t\tif (parts[i] != rhs.parts[i])\n\t\t\t\treturn false;\n\t\treturn true;\n\t}\n\n\tbool operator != (const LNum& rhs) {\n\t\treturn !(*this == rhs);\n\t}\n\n\tfriend ostream& operator<<(ostream& os, const LNum& dt);\n\n\tstatic LNum abs_sub(LNum lhs, LNum rhs) {\n\t\treturn lhs > rhs ? lhs - rhs : rhs - lhs;\n\t}\n\n\t// Miller–Rabin primality test\n\tbool is_prime(int certainty) const {\n\t\tif (*this == 1) return true;\n\t\tif (LNum(2) == *this || LNum(3) == *this)\n\t\t\treturn true;\n\t\tif (LNum(2) > * this || *this % 2 == 0)\n\t\t\treturn false;\n\n\t\tLNum d = *this - 1;\n\t\tint s = 0;\n\n\t\twhile (d % 2 == 0) {\n\t\t\td /= 2;\n\t\t\ts += 1;\n\t\t}\n\n\t\tfor (uint64_t i = 0; i < certainty; ++i) {\n\t\t\tLNum a = LNum::random(2, *this - 3);\n\n\t\t\tLNum x = a.pow_mod(d, *this);\n\t\t\tif (x == 1 || x == *this - 1)\n\t\t\t\tcontinue;\n\n\t\t\tfor (uint64_t r = 1; r < s; ++r) {\n\t\t\t\tx = x.pow_mod(2, *this);\n\t\t\t\tif (x == 1)\n\t\t\t\t\treturn false;\n\t\t\t\tif (x == *this - 1)\n\t\t\t\t\tbreak;\n\t\t\t}\n\n\t\t\tif (x != *this - 1)\n\t\t\t\treturn false;\n\t\t}\n\n\t\treturn true;\n\t}\n\n\tstatic LNum sqrt(LNum x) {\n\t\tLNum r = x;\n\t\tLNum l = 0;\n\t\tLNum res = 0;\n\t\twhile (l <= r)\n\t\t{\n\t\t\tLNum m = (l + r) / 2;\n\t\t\tif (m * m <= x)\n\t\t\t{\n\t\t\t\tres = m;\n\t\t\t\tl = m + 1;\n\t\t\t}\n\t\t\telse {\n\t\t\t\tr = m - 1;\n\t\t\t}\n\t\t}\n\t\treturn res;\n\t}\n\n\tstring to_str() const {\n\t\tstring res;\n\t\tchar buff[BASE_POWER + 1];\n\t\tsnprintf(buff, sizeof(buff), \"%llu\", parts.empty() ? 0 : parts.back());\n\t\tres += buff;\n\t\tfor (ptrdiff_t i = parts.size() - 2; i >= 0; --i) {\n\t\t\tsnprintf(buff, sizeof(buff), (\"%0\" + to_string(BASE_POWER) + \"llu\").c_str(), parts[i]);\n\t\t\tres += buff;\n\t\t}\n\t\treturn res;\n\t}\n\n\tuint64_t to_int() const {\n\t\tif (LNum(numeric_limits::max()) >= *this) {\n\t\t\treturn stoull(this->to_str());\n\t\t}\n\t\telse {\n\t\t\tthrow;\n\t\t}\n\t}\n LNum() {}\nprivate:\n\tstatic void remove_zeros(vector& v) {\n\t\twhile (v.size() > 1 && v.back() == 0)\n\t\t\tv.pop_back();\n\t}\n\n\tvector> decompose(LNum l) {\n\t\tvector> a(N);\n\t\tfor (uint64_t i = 0; i < N; ++i) {\n\t\t\ta[i].resize(P);\n\t\t\tfor (uint64_t j = 0; j < P / 2; ++j) {\n\t\t\t\ta[i][j] = l % std::pow(2, P);\n\t\t\t\tl /= std::pow(2, P);\n\t\t\t}\n\t\t\tfor (uint64_t j = P / 2; j < P; ++j) {\n\t\t\t\ta[i][j] = 0;\n\t\t\t}\n\t\t}\n\t\treturn a;\n\t}\n\n\tLNum compose(vector> a0) {\n\t\tLNum v = 0;\n\t\t//for (int64_t i = 0; i < N; ++i) {\n\t\t//\tfor (int64_t j = 0; j < P; ++j) {\n\t\t//\t\tv.plus(LNum(a0[i][j].real()).mul(LNum(2).pow(i * (P * P / 2) + j * P)));\n\t\t//\t}\n\t\t//}\n\t\tvector> a(N);\n\t\tfor (uint64_t i = 0; i < N; ++i) {\n\t\t\ta[i].resize(P);\n\t\t\ttransform(begin(a0[i]), end(a0[i]), begin(a[i]), [](const Complex& c) { return round(c.real()); });\n\t\t}\n\n\t\tfor (int64_t j = P - 1; j >= P / 2; --j) {\n\t\t\tv = v * uint64_t(std::pow(2, P)) + a[N - 1][j];\n\t\t}\n\t\tfor (int64_t i = N - 1; i >= 1; --i) {\n\t\t\tfor (int64_t j = P / 2 - 1; j >= 0; --j) {\n\t\t\t\tv = v * uint64_t(std::pow(2, P)) + a[i][j] + a[i - 1][j + P / 2];\n\t\t\t}\n\t\t}\n\t\tfor (int64_t j = P / 2 - 1; j >= 0; --j) {\n\t\t\tv = v * uint64_t(std::pow(2, P)) + a[0][j];\n\t\t}\n\t\treturn v;//v.mod(LNum(2).pow(n));\n\t}\n\n\tvector> fft(vector> a, valarray w_, uint64_t N_) {\n\t\tif (N_ == 1) {\n\t\t\treturn a;\n\t\t}\n\t\telse if (N_ == 2) {\n\t\t\tvector> b(N_);\n\t\t\tb[0] = a[0] + a[1];\n\t\t\tb[1] = a[0] - a[1];\n\t\t\treturn b;\n\t\t}\n\n\t\tassert(N_ >= 4);\n\t\tconst uint64_t J = (N_ <= 2 * P) ? 2 : 2 * P;\n\t\tconst uint64_t K = N_ / J;\n\n\t\tvector>> c(K);\n\t\tassert(K > 0);\n\t\tfor (uint64_t k = 0; k < K; ++k) {\n\t\t\tc[k].resize(J);\n\t\t\tfor (uint64_t k1 = 0; k1 < J; ++k1) {\n\t\t\t\tc[k][k1] = a[k1 * K + k];\n\t\t\t}\n\n\t\t\tc[k] = fft(c[k], ::pow(w_, 2), J);\n\t\t}\n\n\t\tvector> b(N_);\n\t\tfor (uint64_t j = 0; j < J; ++j) {\n\t\t\tvector> d_j(K);\n\t\t\tfor (uint64_t k = 0; k < K; ++k) {\n\t\t\t\td_j[k] = c[k][j] * ::pow(w_, j * k);\n\t\t\t}\n\n\t\t\td_j = fft(d_j, ::pow(w_, J), K);\n\n\t\t\tfor (uint64_t j1 = 0; j1 < K; ++j1) {\n\t\t\t\tb[j1 * J + j] = d_j[j1];\n\t\t\t}\n\t\t}\n\n\t\treturn b;\n\t}\n\n\tvector> half_fft(vector> a_real, valarray dzeta) {\n\t\tvector> a(N);\n\t\tfor (size_t i = 0; i < N; ++i) {\n\t\t\ta[i].resize(P);\n\t\t\tfor (size_t j = 0; j < P; ++j) {\n\t\t\t\ta[i][j] = Complex(a_real[i][j], 0);\n\t\t\t}\n\t\t}\n\t\tfor (uint64_t k = 0; k < N; ++k) {\n\t\t\ta[k] *= ::pow(dzeta, k);\n\t\t}\n\t\treturn fft(a, ::pow(dzeta, 2), N);\n\t}\n\n\tvector> inv_half_fft(vector> c, valarray dzeta) {\n\t\tvalarray w = ::pow(dzeta, 2);\n\n\t\tvector> b = fft(c, ::pow(w, -1), N);\n\n\t\tfor (int64_t k = 0; k < N; ++k) {\n\t\t\tb[k] = b[k] * ::pow(dzeta, ldouble(-k)) / N;\n\t\t}\n\n\t\treturn b;\n\t}\n\n\tstatic uint64_t base_max() {\n\t\tuint64_t res = 0;\n\t\tfor (uint64_t i = 0; i < BASE_POWER; ++i) {\n\t\t\tres += 9 * pow(10, i);\n\t\t}\n\t\treturn res;\n\t}\n \n friend class LNumHasher;\n};\n\nclass LNumHasher {\npublic:\n\tsize_t operator()(LNum const& n) const {\n\t\tauto vec = n.parts;\n\t\tsize_t seed = vec.size();\n\t\tconst auto m = uint64_t((sqrtl(5) - 1.l) * powl(2, CHAR_BIT * sizeof(uint64_t) - 1));\n\t\tfor (auto& i : vec) {\n\t\t\tseed ^= i + m + (seed << 6) + (seed >> 2);\n\t\t}\n\t\treturn seed;\n\t}\n};\n\nostream& operator<<(ostream& os, const LNum& ln) {\n\treturn os << ln.to_str();\n}\n\n// Modular multiplicative inverse\n// ax = 1 (mod m)\nLNum mul_inv(LNum a, LNum m) {\n\tLNum b = a % m;\n\tfor (LNum x = 1; x < m; x += 1) {\n\t\tif ((b * x) % m == 1) {\n\t\t\treturn x;\n\t\t}\n\t}\n\tthrow invalid_argument(\"n_i are not pairwise co-prime!\");\n}\n\noptional chinese_remainder(vector n, vector a) {\n\tLNum prod = reduce(std::execution::seq, n.begin(), n.end(), LNum(1), [](LNum a, LNum b) { return a * b; });\n\n\tLNum sum = 0;\n\tfor (size_t i = 0; i < n.size(); ++i) {\n\t\tLNum p = prod / n[i];\n\t\ttry {\n\t\t\tsum += a[i] * mul_inv(p, n[i]) * p;\n\t\t}\n\t\tcatch (invalid_argument) {\n\t\t\treturn nullopt;\n\t\t}\n\t}\n\n\treturn sum % prod;\n}\n\nLNum gcd(LNum a, LNum b) {\n\twhile (b != 0) {\n\t\ta %= b;\n\t\tif (a == 0)\n\t\t\treturn b;\n\t\tb %= a;\n\t}\n\treturn a;\n}\n\nLNum _ro_pollard(LNum n) {\n\tauto f = [](LNum x, LNum n, LNum inc) { return (x * x + inc) % n; };\n\tLNum d = 1;\n\tif (n == 4) return 2;\n\n\tLNum x = 2;\n\tLNum y = 2;\n\tLNum inc = 1;\n\n\tdo {\n\t\tx = f(x, n, inc);\n\t\ty = f(y, n, inc);\n\t\ty = f(y, n, inc);\n\t\td = x == y ? 0 : gcd(LNum::abs_sub(x, y), n);\n\n\t\tif (d == 0) {\n\t\t\tx = 2;\n\t\t\ty = 2;\n\t\t\td = 1;\n\t\t\tinc += 1;\n\t\t}\n\t} while (d == 1 || d == n);\n\treturn d;\n}\n\n// 1. https://ru.wikipedia.org/wiki/%D0%A0%D0%BE-%D0%B0%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC_%D0%9F%D0%BE%D0%BB%D0%BB%D0%B0%D1%80%D0%B4%D0%B0\nvector ro_pollard(LNum n) {\n\tif (n.is_prime(5)) {\n\t\treturn { n };\n\t}\n\n\tLNum left = _ro_pollard(n);\n\tLNum right = n / left;\n\tauto res1 = ro_pollard(left);\n\tauto res2 = ro_pollard(right);\n\n\tres1.insert(res1.end(), res2.begin(), res2.end());\n\treturn res1;\n}\n\n// 2. https://en.wikipedia.org/wiki/Baby-step_giant-step\nLNum babystep_giantstep(LNum g, LNum h, LNum p) {\n\tLNum m = LNum::sqrt(p);\n\tif (p - m * m > 0) m += 1;\n\t\n\tauto table = unordered_map();\n\tLNum e = 1;\n\tfor (LNum i = 0; i < m; i += 1) {\n\t\ttable[e] = i;\n\t\te = (e * g) % p;\n\t}\n\n\tconst LNum factor = g.pow_mod(p - m - 1, p);\n\te = h;\n\tfor (LNum i = 0; i < m; i += 1) {\n\t\tif (auto it = table.find(e); it != table.end() && it->second != 0) {\n\t\t\treturn { i*m + it->second };\n\t\t}\n\t\te = (e * factor) % p;\n\t}\n\t\n\treturn 0;\n}\n\ntemplate \nvector unique(vector v) {\n\tsort(v.begin(), v.end());\n\tv.erase(unique(v.begin(), v.end()), v.end());\n\treturn v;\n}\n\n// 3. https://stackoverflow.com/a/52263174/8390594\nLNum totient(LNum n) {\n\tif (n == 1) return 1;\n\tfor (LNum& factor : unique(ro_pollard(n))) {\n\t\tn -= n / factor;\n\t}\n\treturn n;\n}\n\n// 3. https://www.geeksforgeeks.org/program-mobius-function/\nint16_t mobius(LNum n) {\n\tLNum p = 0;\n\n\tif (n % 2 == 0) {\n\t\tn = n / 2;\n\t\tp += 1;\n\n\t\tif (n % 2 == 0)\n\t\t\treturn 0;\n\t}\n\n\tconst LNum ii = LNum::sqrt(n);\n\tfor (LNum i = 3; i <= ii; i = i + 2) {\n\t\tif (n % i == 0) {\n\t\t\tn = n / i;\n\t\t\tp += 1;\n\n\t\t\tif (n % i == 0)\n\t\t\t\treturn 0;\n\t\t}\n\t}\n\n\treturn (p % 2) ? 1 : -1;\n}\n\n// 4. https://en.wikipedia.org/wiki/Jacobi_symbol\nint16_t jacobi(LNum a, LNum n) {\n\tassert(n > a&& a > 0 && n % 2 == 1);\n\ta %= n;\n\tint8_t res = 1;\n\twhile (a != 0) {\n\t\twhile (a % 2 == 0) {\n\t\t\ta /= 2;\n\t\t\tLNum r = n % 8;\n\t\t\tif (r == 3 || r == 5) res = -res; // 9: (2a | n) = -(a | n) if n = 3, 5 (mod 8) else (a | n)\n\t\t}\n\t\tswap(a, n);\n\t\tif (a % 4 == 3 && n % 4 == 3)\n\t\t\tres = -res; // 6: (a | n) = -(n | a) if n = a = 3 (mod 4) eles (n | a)\n\t\ta %= n;\n\t}\n\tif (n == 1) return res;\n\telse return 0;\n}\n\n// 4. Legendre symbol. Returns 1, 0, or p-1\nLNum legendre1(LNum a, LNum p) {\n\tLNum res = a.pow_mod((p - 1) / 2, p);\n\t// assert(res == legendre2(a, p));\n\treturn res;\n}\n\ntuple mul(tuple aa, tuple bb, LNum p, LNum finalOmega) {\n\treturn make_tuple(\n\t\t(get<0>(aa) * get<0>(bb) + get<1>(aa) * get<1>(bb) * finalOmega) % p,\n\t\t(get<0>(aa) * get<1>(bb) + get<0>(bb) * get<1>(aa)) % p\n\t);\n}\n\n// 5. https://rosettacode.org/wiki/Cipolla%27s_algorithm\noptional> chipolli(LNum n, LNum p) {\n\tif (legendre1(n, p) != 1) {\n\t\treturn make_tuple(0, 0);\n\t}\n\n\tLNum a = 0;\n\tLNum omega2 = 0;\n\twhile (true) {\n\t\tomega2 = (a * a + p - n) % p;\n\t\tif (legendre1(omega2, p) == p - 1) {\n\t\t\tbreak;\n\t\t}\n\t\ta += 1;\n\t}\n\n\t// Step 2: Compute power\n\ttuple r = make_tuple(1, 0);\n\ttuple s = make_tuple(a, 1);\n\tLNum nn = ((p + 1) / 2) % p;\n\twhile (nn > 0) {\n\t\tif (nn % 2 == 1) {\n\t\t\tr = mul(r, s, p, omega2);\n\t\t}\n\t\ts = mul(s, s, p, omega2);\n\t\tnn /= 2;\n\t}\n\n\t// Step 3: Check x in Fp\n\tif (get<1>(r) != 0) {\n\t\treturn nullopt;\n\t}\n\n\t// Step 5: Check x * x = n\n\tif (get<0>(r)* get<0>(r) % p != n) {\n\t\treturn nullopt;\n\t}\n\n\t// Step 4: Solutions\n\treturn make_tuple(get<0>(r), p - get<0>(r));\n}\n\nLNum gen_key(LNum q) {\n\tLNum key = 0;\n\twhile (gcd(q, key = LNum::random(LNum(10) ^ 20, q)) != 1) {}\n\treturn key;\n}\t\n\ntuple, LNum> encrypt(string msg, LNum q, LNum h, LNum g) {\n\tvector en_msg(msg.size());\n\n\tLNum k = gen_key(q);\n\tLNum s = h.pow_mod(k, q);\n\tLNum p = g.pow_mod(k, q);\n\n\tcout << \"g^k used : \" << p << endl;\n\tcout << \"g^ak used : \" << s << endl;\n\tfor (size_t i = 0; i < msg.size(); ++i) {\n\t\ten_msg[i] = s * msg[i];\n\t}\n\t\t\t\n\treturn make_tuple(en_msg, p);\n}\n\nstring decrypt(vector en_msg, LNum p, LNum key, LNum q) {\n\tstring dr_msg;\n\tLNum h = p.pow_mod(key, q);\n\tfor (size_t i = 0; i < en_msg.size(); ++i) {\n\t\tdr_msg += (en_msg[i] / h).to_int();\n\t}\n\treturn dr_msg;\n}\t\n\n\nint main() {\n\t//cout << boolalpha;\n\n\tstring message = \"Hello there!\";\n\tcout << \"Original message: \" << message << endl;\n\n\tLNum q = LNum::random(LNum(10) ^ 20, LNum(10) ^ 50);\n\tLNum g = LNum::random(2, q);\n\tLNum key = gen_key(q);\n\tLNum h = g.pow_mod(key, q);\n\n\tvector en_msg;\n\tLNum p = 0;\n\ttie(en_msg, p) = encrypt(message, q, h, g);\n\n\tcout << \"Decripted message: \" << decrypt(en_msg, p, key, q) << endl;\n\t\n\t// Tests for LNum class\n\t//cout << LNum(\"24523748428\").pow_mod(LNum(\"6500000\"), LNum(\"98723459723\")) << '\\n'; //88398031434 3007310280\n\t//cout << \"123456789876543212345678987654321 * 159753579515975357951: \" << LNum(\"123456789876543212345678987654321\") * LNum(\"159753579515975357951\") << '\\n';\n\t//cout << \"sqrt(9^40): \" << sqrt(LNum(\"147808829414345923316083210206383297601\")).to_str() << '\\n';\n\t//cout << \"9^20: \" << (LNum(\"9\")^20).to_str() << '\\n';\n\t//cout << \"10^20+1 > 10^20: \" << (((LNum(\"10\")^20) < LNum(\"10\")^20 + 1) ? \"true\" : \"false\") << '\\n';\n\t//cout << \"1234567^1234: \" << (LNum(\"1234567\") ^ LNum(\"1234\")) << '\\n';\n\n\t// Pollard's rho algorithm test\n\t/*LNum x(\"17348256187264213649126346457\");\n\tfor (LNum& factor : ro_pollard(x)) {\n\t\tcout << factor << ' ';\n\t}\n\tcout << endl;*/\n\n\t// Baby-step giant-step algorithm test\n\t//cout << babystep_giantstep(3, 1, 196134577) << endl;\n\n\t// Euler function test\n\t//cout << totient(1000) << endl;\n\n\t// Mobius function test\n\t//cout << mobius(1234891) << endl;\n\n\t// Legendre symbol test\n\t//cout << legendre1(30, 109) << endl;\n\t//cout << legendre1(30, 127) << endl;\n\n\t// Jacobi symbol test\n\t//cout << jacobi(1001, 9907) << endl;\n\t//cout << jacobi(19, 45) << endl;\n\n\t// Chipolli alpgorithm\n\t/*auto sqrts = chipolli(LNum(\"34035243914635549601583369544560650254325084643201\"), (LNum(10) ^ 50) + 151);\n\tif (sqrts.has_value()) \n\t\tcout << get<0>(sqrts.value()) << ' ' << get<1>(sqrts.value()) << endl;*/\n\n\t// Chinese remainder solver\n\t/*cout << \"x = 16 (mod 17)\\n\";\n\tcout << \"x = 22 (mod 23)\\n\";\n\tcout << \"x = 30 (mod 31)\\n\";\n\tvector n = { 17, 23, 31 };\n\tvector a = { 16, 22, 30 };\n\tauto solution = chinese_remainder(n, a);\n\tcout << (solution.has_value() ? solution.value().to_str() : \"No solution\") << endl;*/\n}\n","codes",[],"stdin","compiler","boost-1.71.0-gcc-head,gnu++2a,cpp-no-pedantic","createdAt",1576467888,"title","description","isPrivate","compilerInfo",{"_11":332,"_13":3356,"_15":333,"_17":18,"_19":3357,"_22":23,"_24":25,"_26":335,"_28":3358},"10.0.0 20191210 (experimental)",[99],[3359,3361,3363,3365,3429,3434,3439,3453],{"_31":32,"_33":3360},{"_11":35,"_36":23,"_37":38,"_17":39},{"_31":32,"_33":3362},{"_11":42,"_36":25,"_37":43,"_17":44},{"_31":32,"_33":3364},{"_11":47,"_36":25,"_37":48,"_17":49},{"_31":51,"_33":3366},{"_11":345,"_36":3367,"_55":3368},"boost-1.71.0-gcc-head",[3369,3370,3374,3378,3382,3386,3390,3394,3398,3402,3406,3410,3414,3418,3422,3426],{"_11":346,"_37":59,"_17":330},{"_11":3371,"_37":3372,"_17":3373},"boost-1.58.0-gcc-head","-I/opt/wandbox/boost-1.58.0/gcc-head/include","Boost 1.58.0",{"_11":3375,"_37":3376,"_17":3377},"boost-1.59.0-gcc-head","-I/opt/wandbox/boost-1.59.0/gcc-head/include","Boost 1.59.0",{"_11":3379,"_37":3380,"_17":3381},"boost-1.60.0-gcc-head","-I/opt/wandbox/boost-1.60.0/gcc-head/include","Boost 1.60.0",{"_11":3383,"_37":3384,"_17":3385},"boost-1.61.0-gcc-head","-I/opt/wandbox/boost-1.61.0/gcc-head/include","Boost 1.61.0",{"_11":3387,"_37":3388,"_17":3389},"boost-1.62.0-gcc-head","-I/opt/wandbox/boost-1.62.0/gcc-head/include","Boost 1.62.0",{"_11":3391,"_37":3392,"_17":3393},"boost-1.63.0-gcc-head","-I/opt/wandbox/boost-1.63.0/gcc-head/include","Boost 1.63.0",{"_11":3395,"_37":3396,"_17":3397},"boost-1.64.0-gcc-head","-I/opt/wandbox/boost-1.64.0/gcc-head/include","Boost 1.64.0",{"_11":3399,"_37":3400,"_17":3401},"boost-1.65.0-gcc-head","-I/opt/wandbox/boost-1.65.0/gcc-head/include","Boost 1.65.0",{"_11":3403,"_37":3404,"_17":3405},"boost-1.65.1-gcc-head","-I/opt/wandbox/boost-1.65.1/gcc-head/include","Boost 1.65.1",{"_11":3407,"_37":3408,"_17":3409},"boost-1.66.0-gcc-head","-I/opt/wandbox/boost-1.66.0/gcc-head/include","Boost 1.66.0",{"_11":3411,"_37":3412,"_17":3413},"boost-1.67.0-gcc-head","-I/opt/wandbox/boost-1.67.0/gcc-head/include","Boost 1.67.0",{"_11":3415,"_37":3416,"_17":3417},"boost-1.68.0-gcc-head","-I/opt/wandbox/boost-1.68.0/gcc-head/include","Boost 1.68.0",{"_11":3419,"_37":3420,"_17":3421},"boost-1.69.0-gcc-head","-I/opt/wandbox/boost-1.69.0/gcc-head/include","Boost 1.69.0",{"_11":3423,"_37":3424,"_17":3425},"boost-1.70.0-gcc-head","-I/opt/wandbox/boost-1.70.0/gcc-head/include","Boost 1.70.0",{"_11":3367,"_37":3427,"_17":3428},"-I/opt/wandbox/boost-1.71.0/gcc-head/include","Boost 1.71.0",{"_31":32,"_33":3430},{"_11":3431,"_36":25,"_37":3432,"_17":3433},"sprout","-I/opt/wandbox/sprout","Sprout",{"_31":32,"_33":3435},{"_11":3436,"_36":25,"_37":3437,"_17":3438},"msgpack","-I/opt/wandbox/msgpack/include","MessagePack",{"_31":51,"_33":3440},{"_11":351,"_36":393,"_55":3441},[3442,3443,3444,3445,3446,3447,3448,3449,3450,3451,3452],{"_11":355,"_37":59,"_17":60},{"_11":357,"_37":358,"_17":359},{"_11":361,"_37":362,"_17":363},{"_11":365,"_37":366,"_17":367},{"_11":369,"_37":370,"_17":371},{"_11":373,"_37":374,"_17":375},{"_11":377,"_37":378,"_17":379},{"_11":381,"_37":382,"_17":383},{"_11":385,"_37":386,"_17":387},{"_11":389,"_37":390,"_17":391},{"_11":393,"_37":394,"_17":395},{"_31":51,"_33":3454},{"_11":86,"_36":87,"_55":3455},[3456,3457,3458],{"_11":87,"_37":59,"_17":90},{"_11":86,"_37":92,"_17":92},{"_11":94,"_37":95,"_17":95},"results",[3461,3465,3468,3471],{"_31":3462,"_3463":3464},"Control","data","Start",{"_31":3466,"_3463":3467},"StdOut","Original message: Hello there!\ng^k used : 29970601577636059995799388913700745694887220566505\ng^ak used : 28081554322951008853918343252693778158435121663765\nDecripted message: Hello there!\n",{"_31":3469,"_3463":3470},"ExitCode","0",{"_31":3462,"_3463":3472},"Finish","env",{"_3475":3476,"_3477":3478,"_3479":3480,"_3481":3482,"_3483":3484,"_3485":3486},"KV_CACHE",{},"KV_SESSION",{},"WANDBOX_GITHUB_CLIENT_ID","f9d429d939d997e6b08e","WANDBOX_GITHUB_CLIENT_SECRET","d99b3d12225671cde514d9e2b3d5cc8356f4ed5f","WANDBOX_KV_COOKIE_SECRET","FaCnykHoYzqiXReGkgvmcYGvQdQ4yZUE","WANDBOX_URL_PREFIX","https://api.wandbox.org","root","actionData","errors"]