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#define PROBLEM "https://yukicoder.me/problems/no/502" #include "../../template/template.hpp" #include "../../math/combinatorics/mod-int.hpp" #include "../../math/combinatorics/factorial.hpp" #include "../../math/fft/arbitrary-mod-convolution.hpp" const int MOD = (int) (1e9 + 7); using mint = ModInt< MOD >; int main() { int N; cin >> N; ArbitraryModConvolution< mint > fft; auto f = [&](vector< mint > &a, vector< mint > &b) { return fft.multiply(a, b); }; cout << factorial< mint >(N, f) << "\n"; }
#line 1 "test/verify/yukicoder-502.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/502" #line 1 "template/template.hpp" #include<bits/stdc++.h> using namespace std; using int64 = long long; const int mod = 1e9 + 7; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 >& p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { explicit FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } #line 4 "test/verify/yukicoder-502.test.cpp" #line 1 "math/combinatorics/mod-int.hpp" template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; using modint = ModInt< mod >; #line 1 "math/combinatorics/enumeration.hpp" /** * @brief Enumeration(組み合わせ) */ template< typename T > struct Enumeration { private: static vector< T > _fact, _finv, _inv; inline static void expand(size_t sz) { if(_fact.size() < sz + 1) { int pre_sz = max(1, (int) _fact.size()); _fact.resize(sz + 1, T(1)); _finv.resize(sz + 1, T(1)); _inv.resize(sz + 1, T(1)); for(int i = pre_sz; i <= (int) sz; i++) { _fact[i] = _fact[i - 1] * T(i); } _finv[sz] = T(1) / _fact[sz]; for(int i = (int) sz - 1; i >= pre_sz; i--) { _finv[i] = _finv[i + 1] * T(i + 1); } for(int i = pre_sz; i <= (int) sz; i++) { _inv[i] = _finv[i] * _fact[i - 1]; } } } public: explicit Enumeration(size_t sz = 0) { expand(sz); } static inline T fact(int k) { expand(k); return _fact[k]; } static inline T finv(int k) { expand(k); return _finv[k]; } static inline T inv(int k) { expand(k); return _inv[k]; } static T P(int n, int r) { if(r < 0 || n < r) return 0; return fact(n) * finv(n - r); } static T C(int p, int q) { if(q < 0 || p < q) return 0; return fact(p) * finv(q) * finv(p - q); } static T H(int n, int r) { if(n < 0 || r < 0) return 0; return r == 0 ? 1 : C(n + r - 1, r); } }; template< typename T > vector< T > Enumeration< T >::_fact = vector< T >(); template< typename T > vector< T > Enumeration< T >::_finv = vector< T >(); template< typename T > vector< T > Enumeration< T >::_inv = vector< T >(); #line 2 "math/combinatorics/sample-point-shift.hpp" /** * @brief Sample Point Shift(標本点シフト) */ template< typename Mint, typename F > vector< Mint > sample_point_shift(const vector< Mint > &ys, const Mint &m, const F &multiply) { Enumeration< Mint > comb; int d = (int) ys.size() - 1; vector< Mint > f(d + 1), g(d * 2 + 1); for(int i = 0; i <= d; i++) { f[i] = ys[i] * comb.finv(i) * comb.finv(d - i); if((d - i) & 1) f[i] = -f[i]; } for(int i = 0; i <= 2 * d; i++) { g[i] = Mint(1) / (m - d + i); } auto h = multiply(f, g); Mint coef = 1; for(int i = 0; i <= d; i++) { coef *= (m - d + i); } for(int i = 0; i <= d; i++) { h[i + d] *= coef; coef *= (m + i + 1) * g[i]; } return vector< Mint >{begin(h) + d, begin(h) + 2 * d + 1}; } #line 2 "math/combinatorics/factorial.hpp" /** * @brief Factorial(階乗) */ template< typename Mint, typename F > Mint factorial(int64_t n, const F& multiply) { if(n <= 1) return 1; if(n >= Mint::get_mod()) return 0; int64_t v = 1; while(v * v < n) v *= 2; Mint iv = Mint(1) / v; vector< Mint > G{1, v + 1}; for(int64_t d = 1; d != v; d <<= 1) { vector< Mint > G1 = sample_point_shift(G, Mint(d) * iv, multiply); vector< Mint > G2 = sample_point_shift(G, Mint(d * v + v) * iv, multiply); vector< Mint > G3 = sample_point_shift(G, Mint(d * v + d + v) * iv, multiply); for(int i = 0; i <= d; i++) G[i] *= G1[i], G2[i] *= G3[i]; copy(begin(G2), end(G2) - 1, back_inserter(G)); } Mint res = 1; int64_t i = 0; while(i + v <= n) res *= G[i / v], i += v; while(i < n) res *= ++i; return res; } #line 7 "test/verify/yukicoder-502.test.cpp" #line 1 "math/fft/fast-fourier-transform.hpp" namespace FastFourierTransform { using real = double; struct C { real x, y; C() : x(0), y(0) {} C(real x, real y) : x(x), y(y) {} inline C operator+(const C &c) const { return C(x + c.x, y + c.y); } inline C operator-(const C &c) const { return C(x - c.x, y - c.y); } inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); } inline C conj() const { return C(x, -y); } }; const real PI = acosl(-1); int base = 1; vector< C > rts = { {0, 0}, {1, 0} }; vector< int > rev = {0, 1}; void ensure_base(int nbase) { if(nbase <= base) return; rev.resize(1 << nbase); rts.resize(1 << nbase); for(int i = 0; i < (1 << nbase); i++) { rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1)); } while(base < nbase) { real angle = PI * 2.0 / (1 << (base + 1)); for(int i = 1 << (base - 1); i < (1 << base); i++) { rts[i << 1] = rts[i]; real angle_i = angle * (2 * i + 1 - (1 << base)); rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i)); } ++base; } } void fft(vector< C > &a, int n) { assert((n & (n - 1)) == 0); int zeros = __builtin_ctz(n); ensure_base(zeros); int shift = base - zeros; for(int i = 0; i < n; i++) { if(i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for(int k = 1; k < n; k <<= 1) { for(int i = 0; i < n; i += 2 * k) { for(int j = 0; j < k; j++) { C z = a[i + j + k] * rts[j + k]; a[i + j + k] = a[i + j] - z; a[i + j] = a[i + j] + z; } } } } vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) { int need = (int) a.size() + (int) b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; vector< C > fa(sz); for(int i = 0; i < sz; i++) { int x = (i < (int) a.size() ? a[i] : 0); int y = (i < (int) b.size() ? b[i] : 0); fa[i] = C(x, y); } fft(fa, sz); C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0); for(int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r; fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r; fa[i] = z; } for(int i = 0; i < (sz >> 1); i++) { C A0 = (fa[i] + fa[i + (sz >> 1)]) * t; C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i]; fa[i] = A0 + A1 * s; } fft(fa, sz >> 1); vector< int64_t > ret(need); for(int i = 0; i < need; i++) { ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x); } return ret; } }; #line 2 "math/fft/arbitrary-mod-convolution.hpp" /* * @brief Arbitrary Mod Convolution(任意mod畳み込み) */ template< typename T > struct ArbitraryModConvolution { using real = FastFourierTransform::real; using C = FastFourierTransform::C; ArbitraryModConvolution() = default; static vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) { if(need == -1) need = a.size() + b.size() - 1; int nbase = 0; while((1 << nbase) < need) nbase++; FastFourierTransform::ensure_base(nbase); int sz = 1 << nbase; vector< C > fa(sz); for(int i = 0; i < a.size(); i++) { fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15); } fft(fa, sz); vector< C > fb(sz); if(a == b) { fb = fa; } else { for(int i = 0; i < b.size(); i++) { fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15); } fft(fb, sz); } real ratio = 0.25 / sz; C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1); for(int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); C a1 = (fa[i] + fa[j].conj()); C a2 = (fa[i] - fa[j].conj()) * r2; C b1 = (fb[i] + fb[j].conj()) * r3; C b2 = (fb[i] - fb[j].conj()) * r4; if(i != j) { C c1 = (fa[j] + fa[i].conj()); C c2 = (fa[j] - fa[i].conj()) * r2; C d1 = (fb[j] + fb[i].conj()) * r3; C d2 = (fb[j] - fb[i].conj()) * r4; fa[i] = c1 * d1 + c2 * d2 * r5; fb[i] = c1 * d2 + c2 * d1; } fa[j] = a1 * b1 + a2 * b2 * r5; fb[j] = a1 * b2 + a2 * b1; } fft(fa, sz); fft(fb, sz); vector< T > ret(need); for(int i = 0; i < need; i++) { int64_t aa = llround(fa[i].x); int64_t bb = llround(fb[i].x); int64_t cc = llround(fa[i].y); aa = T(aa).x, bb = T(bb).x, cc = T(cc).x; ret[i] = aa + (bb << 15) + (cc << 30); } return ret; } }; #line 9 "test/verify/yukicoder-502.test.cpp" const int MOD = (int) (1e9 + 7); using mint = ModInt< MOD >; int main() { int N; cin >> N; ArbitraryModConvolution< mint > fft; auto f = [&](vector< mint > &a, vector< mint > &b) { return fft.multiply(a, b); }; cout << factorial< mint >(N, f) << "\n"; }