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time m of each t if launch at time x:\n x\\t 9 3 7 6 11 total\n 0 3 1 1 2 1 8\n 1 0 2 2 3 2 9\n 2 1 3 3 0 3 10\n 3 2 0 0 1 0 3\nWe see that if x increases by 1, all wait times will also increase by 1,\n but wrap around so they'll never be >= d (constant time between launches)\nIf we pre-calculate and group people with same wait time if launch at time 0:\n m0 0 1 2 3\n f 0 3 1 1\nand also collect total wait time if launch at time 0:\n w[0] = 1*3 + 2*1 + 3*1 = 8\nWe can calculate total wait time if launch at time 1, which is total wait time\n if launch at time 0, plus n (n wait times increase by 1), and minus d\n times number of people at m0 = 3\n w[1] = w[0] + n - d*f[3]\nThe number 3 in f[3] can be deduce to be d - k: 3 = 4 - 1. Indeed if we\n jumps from k=1 to k=2, f[d - 2] is the one to be wrapped around (t=6 in\n the above example).\nSo we have the formula for w[2]:\n w[2] = w[1] + n - d*f[d - 2]\nwhich we can substitue w[1] to get:\n w[2] = (w[0] + n - d*f[d - 1]) + n - d*f[d - 2]\n = w[0] + 2n - d*(f[d - 1] + f[d - 2])\nFinally we have the general formula:\n w[k] = w[0] + k*n - d*(f[d-1] + f[d-2] + ... + f[d-k])\n*/\n\n#include \n#include \n#include \n\nint main()\n{\n int n, d;\n std::cin >> n >> d;\n\n //\n // Group ppl w/ same wait time if launch at time 0\n // Wait time (if launch at time 0) formula:\n // m0 = d - (t % d), if m0 == t then m0 = 0\n // or m0 = (d - (t % d)) % d\n //\n std::map> f;\n for (int t; std::cin >> t;)\n f[(d - t % d) % d]++;\n\n //\n // Calculate initial total wait time w[0]\n //\n int64_t w0 = 0;\n for (auto [m, fm] : f)\n w0 += (int64_t)m * fm;\n\n //\n // Find launch time x that minimize total wait time w\n // Total wait time w[k] if launch at time k formula:\n // w[k] = 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