#include #include #include #include #include #include using namespace std; using u64 = uint64_t; template class BIT { int N; vector dat; public: explicit BIT(int n) : N(n+2), dat(N) {} void add(int k, T x) { for(int i=k+1; i(powl(10, BASE_DIGITS)); inline constexpr u64 O = 7, M = (1ULL << 63) - (1ULL << 41) + 1, M2 = M - 2; inline constexpr u64 mod_mul(__uint128_t x, u64 y) { return static_cast(x * y % M); } map, u64> cache; inline u64 mod_pow(u64 a, u64 n) { auto key = make_pair(a, n); if(cache.count(key)) { return cache[key]; } u64 res = 1; for(; n; n>>=1) { if(n & 1) { res = mod_mul(res, a); } a = mod_mul(a, a); } return cache[key] = res; } void myfmt(vector &a, bool inv) { size_t n = a.size(); if(n == 1) { return; } size_t m = n / 2; vector a0(m), a1(m); for(size_t i=0, j=0; i= M) { a[k] -= M; } pz = mod_mul(pz, z); } for(size_t i=0, k=m; k= M) { a[k] -= M; } pz = mod_mul(pz, z); } } void fmt(vector &a) { myfmt(a, false); } void ifmt(vector &a) { myfmt(a, true); size_t n = a.size(); u64 inv = mod_pow(n, M2); for(size_t i=0; i convol(const vector &A, const vector &B) { vector a = A, b = B; size_t n = 1; while(n < a.size() + b.size()) { n <<= 1; } a.resize(n); b.resize(n); fmt(a); fmt(b); vector c(n); for(size_t i=0; i 1) { c.pop_back(); --n; } return c; } vector add(const vector &A, const vector &B) { vector a = A, b = B; size_t N = max(a.size(), b.size()); a.resize(N); b.resize(N); vector c(N); for(size_t i=0; i v; pair, vector> f(int lo, int hi) { if(hi - lo == 1) { return {{v[lo]}, {static_cast(lo+1)}}; } int md = (lo + hi) / 2; auto [x0, x1] = f(lo, md); auto [y0, y1] = f(md, hi); return {add(convol(y0, x1), x0), convol(x1, y1)}; } void print(vector &a) { size_t n = a.size(); reverse(a.begin(), a.end()); printf("%lu", a[0]); for(size_t i=1; i tree(N); v.resize(N); vector p(N); for(int i=0; i r = add(f(0, N).first, vector(1, 1)); print(r); return 0; }