結果
問題 | No.1035 Color Box |
ユーザー |
![]() |
提出日時 | 2020-04-24 22:48:46 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 24 ms / 2,000 ms |
コード長 | 16,014 bytes |
コンパイル時間 | 2,654 ms |
コンパイル使用メモリ | 207,460 KB |
最終ジャッジ日時 | 2025-01-10 00:18:54 |
ジャッジサーバーID (参考情報) |
judge5 / judge5 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 36 |
ソースコード
#include<bits/stdc++.h>#define rep(i,a) for(int i=(int)0;i<(int)a;++i)#define rrep(i,a) for(int i=(int)a-1;i>=0;--i)#define REP(i,a,b) for(int i=(int)a;i<(int)b;++i)#define RREP(i,a,b) for(int i=(int)a-1;i>=b;--i)#define pb push_back#define eb emplace_back#define all(x) x.begin(),x.end()#define rall(x) x.rbegin(),x.rend()typedef std::vector<int> vi;typedef std::vector<std::vector<int>> vvi;typedef std::vector<long long> vl;typedef std::vector<std::vector<long long>> vvl;#define out(x) cout<<x<<"\n";using ll=long long;constexpr ll mod = 1e9 + 7;constexpr ll INF = 1LL << 60;template<class T> inline bool chmin(T& a, T b) {if (a > b) {a = b;return true;}return false;}template<class T> inline bool chmax(T& a, T b) {if (a < b) {a = b;return true;}return false;}ll gcd(ll n, ll m) {ll tmp;while (m!=0) {tmp = n % m;n = m;m = tmp;}return n;}ll lcm(ll n, ll m) {return abs(n) / gcd(n, m)*abs(m);//gl=xy}using namespace std;#define int64_t lltemplate< 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 >;template< typename T >struct Combination {vector< T > _fact, _rfact, _inv;Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {_fact[0] = _rfact[sz] = _inv[0] = 1;for(int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;_rfact[sz] /= _fact[sz];for(int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);for(int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];}inline T fact(int k) const { return _fact[k]; }inline T rfact(int k) const { return _rfact[k]; }inline T inv(int k) const { return _inv[k]; }T P(int n, int r) const {if(r < 0 || n < r) return 0;return fact(n) * rfact(n - r);}T C(int p, int q) const {if(q < 0 || p < q) return 0;return fact(p) * rfact(q) * rfact(p - q);}T H(int n, int r) const {if(n < 0 || r < 0) return (0);return r == 0 ? 1 : C(n + r - 1, r);}};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;}};template< typename T >struct ArbitraryModConvolution {using real = FastFourierTransform::real;using C = FastFourierTransform::C;ArbitraryModConvolution() = default;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;}};template< typename T >struct FormalPowerSeries : vector< T > {using vector< T >::vector;using P = FormalPowerSeries;using MULT = function< P(P, P) >;static MULT &get_mult() {static MULT mult = nullptr;return mult;}static void set_fft(MULT f) {get_mult() = f;}void shrink() {while(this->size() && this->back() == T(0)) this->pop_back();}P operator+(const P &r) const { return P(*this) += r; }P operator+(const T &v) const { return P(*this) += v; }P operator-(const P &r) const { return P(*this) -= r; }P operator-(const T &v) const { return P(*this) -= v; }P operator*(const P &r) const { return P(*this) *= r; }P operator*(const T &v) const { return P(*this) *= v; }P operator/(const P &r) const { return P(*this) /= r; }P operator%(const P &r) const { return P(*this) %= r; }P &operator+=(const P &r) {if(r.size() > this->size()) this->resize(r.size());for(int i = 0; i < r.size(); i++) (*this)[i] += r[i];return *this;}P &operator+=(const T &r) {if(this->empty()) this->resize(1);(*this)[0] += r;return *this;}P &operator-=(const P &r) {if(r.size() > this->size()) this->resize(r.size());for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i];shrink();return *this;}P &operator-=(const T &r) {if(this->empty()) this->resize(1);(*this)[0] -= r;shrink();return *this;}P &operator*=(const T &v) {const int n = (int) this->size();for(int k = 0; k < n; k++) (*this)[k] *= v;return *this;}P &operator*=(const P &r) {if(this->empty() || r.empty()) {this->clear();return *this;}assert(get_mult() != nullptr);return *this = get_mult()(*this, r);}P &operator%=(const P &r) {return *this -= *this / r * r;}P operator-() const {P ret(this->size());for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];return ret;}P &operator/=(const P &r) {if(this->size() < r.size()) {this->clear();return *this;}int n = this->size() - r.size() + 1;return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);}P pre(int sz) const {return P(begin(*this), begin(*this) + min((int) this->size(), sz));}P operator>>(int sz) const {if(this->size() <= sz) return {};P ret(*this);ret.erase(ret.begin(), ret.begin() + sz);return ret;}P operator<<(int sz) const {P ret(*this);ret.insert(ret.begin(), sz, T(0));return ret;}P rev(int deg = -1) const {P ret(*this);if(deg != -1) ret.resize(deg, T(0));reverse(begin(ret), end(ret));return ret;}P diff() const {const int n = (int) this->size();P ret(max(0, n - 1));for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);return ret;}P integral() const {const int n = (int) this->size();P ret(n + 1);ret[0] = T(0);for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);return ret;}// F(0) must not be 0P inv(int deg = -1) const {assert(((*this)[0]) != T(0));const int n = (int) this->size();if(deg == -1) deg = n;P ret({T(1) / (*this)[0]});for(int i = 1; i < deg; i <<= 1) {ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);}return ret.pre(deg);}// F(0) must be 1P log(int deg = -1) const {assert((*this)[0] == 1);const int n = (int) this->size();if(deg == -1) deg = n;return (this->diff() * this->inv(deg)).pre(deg - 1).integral();}P sqrt(int deg = -1) const {const int n = (int) this->size();if(deg == -1) deg = n;if((*this)[0] == T(0)) {for(int i = 1; i < n; i++) {if((*this)[i] != T(0)) {if(i & 1) return {};if(deg - i / 2 <= 0) break;auto ret = (*this >> i).sqrt(deg - i / 2) << (i / 2);if(ret.size() < deg) ret.resize(deg, T(0));return ret;}}return P(deg, 0);}P ret({T(1)});T inv2 = T(1) / T(2);for(int i = 1; i < deg; i <<= 1) {ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;}return ret.pre(deg);}// F(0) must be 0P exp(int deg = -1) const {assert((*this)[0] == T(0));const int n = (int) this->size();if(deg == -1) deg = n;P ret({T(1)});for(int i = 1; i < deg; i <<= 1) {ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);}return ret.pre(deg);}P pow(int64_t k, int deg = -1) const {const int n = (int) this->size();if(deg == -1) deg = n;for(int i = 0; i < n; i++) {if((*this)[i] != T(0)) {T rev = T(1) / (*this)[i];P C(*this * rev);P D(n - i);for(int j = i; j < n; j++) D[j - i] = C[j];D = (D.log() * k).exp() * (*this)[i].pow(k);P E(deg);if(i * k > deg) return E;auto S = i * k;for(int j = 0; j + S < deg && j < D.size(); j++) E[j + S] = D[j];return E;}}return *this;}T eval(T x) const {T r = 0, w = 1;for(auto &v : *this) {r += w * v;w *= x;}return r;}};template< typename T >T factorial(int64_t n) {if(n >= T::get_mod()) return 0;if(n == 0) return 1;const int64_t sn = sqrt(n);const T sn_inv = T(1) / sn;Combination< modint > comb(sn);using P = vector< T >;ArbitraryModConvolution< T > fft;using FPS = FormalPowerSeries< T >;auto mult = [&](const typename FPS::P &a, const typename FPS::P &b) {auto ret = fft.multiply(a, b);return typename FPS::P(ret.begin(), ret.end());};FPS::set_fft(mult);auto shift = [&](const P &f, T dx) {int n = (int) f.size();T a = dx * sn_inv;auto p1 = P(f);for(int i = 0; i < n; i++) {T d = comb.rfact(i) * comb.rfact((n - 1) - i);if(((n - 1 - i) & 1)) d = -d;p1[i] *= d;}auto p2 = P(2 * n);for(int i = 0; i < p2.size(); i++) {p2[i] = (a.x + i - n) <= 0 ? 1 : a + i - n;}for(int i = 1; i < p2.size(); i++) {p2[i] *= p2[i - 1];}T prod = p2[2 * n - 1];T prod_inv = T(1) / prod;for(int i = 2 * n - 1; i > 0; --i) {p2[i] = prod_inv * p2[i - 1];prod_inv *= a + i - n;}p2[0] = prod_inv;auto p3 = fft.multiply(p1, p2, (int) p2.size());p1 = P(p3.begin() + p1.size(), p3.begin() + p2.size());prod = 1;for(int i = 0; i < n; i++) {prod *= a + n - 1 - i;}for(int i = n - 1; i >= 0; --i) {p1[i] *= prod;prod *= p2[n + i] * (a + i - n);}return p1;};function< P(int) > rec = [&](int64_t n) {if(n == 1) return P({1, 1 + sn});int64_t nh = n >> 1;auto a1 = rec(nh);auto a2 = shift(a1, nh);auto b1 = shift(a1, sn * nh);auto b2 = shift(a1, sn * nh + nh);for(int i = 0; i <= nh; i++) a1[i] *= a2[i];for(int i = 1; i <= nh; i++) a1.emplace_back(b1[i] * b2[i]);if(n & 1) {for(int64_t i = 0; i < n; i++) {a1[i] *= n + 1LL * sn * i;}T prod = 1;for(int64_t i = 1LL * n * sn; i < 1LL * n * sn + n; i++) {prod *= (i + 1);}a1.push_back(prod);}return a1;};auto vs = rec(sn);T ret = 1;for(int64_t i = 0; i < sn; i++) ret *= vs[i];for(int64_t i = 1LL * sn * sn + 1; i <= n; i++) ret *= i;return ret;}void solve(){ll n,m;cin >> n >> m;modint ans = 0;Combination<modint> c(m + 5);modint sum = 0;rep(i,m){modint x = -1;modint y = m - i;ans += x.pow(i) * c.C(m, i) * y.pow(n);}cout << ans << endl;}int main(){ios::sync_with_stdio(false);cin.tie(0);cout<<fixed<<setprecision(15);solve();return 0;}