結果
問題 | No.802 だいたい等差数列 |
ユーザー |
|
提出日時 | 2024-01-13 21:27:19 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 49 ms / 2,000 ms |
コード長 | 19,696 bytes |
コンパイル時間 | 2,178 ms |
コンパイル使用メモリ | 201,216 KB |
最終ジャッジ日時 | 2025-02-18 19:53:18 |
ジャッジサーバーID (参考情報) |
judge2 / judge2 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 30 |
ソースコード
#include <bits/stdc++.h>using namespace std;#define repd(i,a,b) for (ll i=(a);i<(b);i++)#define rep(i,n) repd(i,0,n)#define all(x) (x).begin(),(x).end()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; }typedef long long ll;typedef pair<ll,ll> P;typedef vector<ll> vec;typedef vector<vec> Graph;const long long INF = 1LL<<60;const long long MOD = 1000000007;//https://nyaannyaan.github.io/library/template <typename mint>struct FormalPowerSeries : vector<mint> {using vector<mint>::vector;using FPS = FormalPowerSeries;FPS &operator+=(const FPS &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];return *this;}FPS &operator+=(const mint &r) {if (this->empty()) this->resize(1);(*this)[0] += r;return *this;}FPS &operator-=(const FPS &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];return *this;}FPS &operator-=(const mint &r) {if (this->empty()) this->resize(1);(*this)[0] -= r;return *this;}FPS &operator*=(const mint &v) {for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;return *this;}FPS &operator/=(const FPS &r) {if (this->size() < r.size()) {this->clear();return *this;}int n = this->size() - r.size() + 1;if ((int)r.size() <= 64) {FPS f(*this), g(r);g.shrink();mint coeff = g.back().inverse();for (auto &x : g) x *= coeff;int deg = (int)f.size() - (int)g.size() + 1;int gs = g.size();FPS quo(deg);for (int i = deg - 1; i >= 0; i--) {quo[i] = f[i + gs - 1];for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];}*this = quo * coeff;this->resize(n, mint(0));return *this;}return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();}FPS &operator%=(const FPS &r) {*this -= *this / r * r;shrink();return *this;}FPS operator+(const FPS &r) const { return FPS(*this) += r; }FPS operator+(const mint &v) const { return FPS(*this) += v; }FPS operator-(const FPS &r) const { return FPS(*this) -= r; }FPS operator-(const mint &v) const { return FPS(*this) -= v; }FPS operator*(const FPS &r) const { return FPS(*this) *= r; }FPS operator*(const mint &v) const { return FPS(*this) *= v; }FPS operator/(const FPS &r) const { return FPS(*this) /= r; }FPS operator%(const FPS &r) const { return FPS(*this) %= r; }FPS operator-() const {FPS ret(this->size());for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];return ret;}void shrink() {while (this->size() && this->back() == mint(0)) this->pop_back();}FPS rev() const {FPS ret(*this);reverse(begin(ret), end(ret));return ret;}FPS dot(FPS r) const {FPS ret(min(this->size(), r.size()));for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];return ret;}FPS pre(int sz) const {return FPS(begin(*this), begin(*this) + min((int)this->size(), sz));}FPS operator>>(int sz) const {if ((int)this->size() <= sz) return {};FPS ret(*this);ret.erase(ret.begin(), ret.begin() + sz);return ret;}FPS operator<<(int sz) const {FPS ret(*this);ret.insert(ret.begin(), sz, mint(0));return ret;}FPS diff() const {const int n = (int)this->size();FPS ret(max(0, n - 1));mint one(1), coeff(1);for (int i = 1; i < n; i++) {ret[i - 1] = (*this)[i] * coeff;coeff += one;}return ret;}FPS integral() const {const int n = (int)this->size();FPS ret(n + 1);ret[0] = mint(0);if (n > 0) ret[1] = mint(1);auto mod = mint::get_mod();for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];return ret;}mint eval(mint x) const {mint r = 0, w = 1;for (auto &v : *this) r += w * v, w *= x;return r;}FPS log(int deg = -1) const {assert((*this)[0] == mint(1));if (deg == -1) deg = (int)this->size();return (this->diff() * this->inv(deg)).pre(deg - 1).integral();}FPS pow(int64_t k, int deg = -1) const {const int n = (int)this->size();if (deg == -1) deg = n;if (k == 0) {FPS ret(deg);if (deg) ret[0] = 1;return ret;}for (int i = 0; i < n; i++) {if ((*this)[i] != mint(0)) {mint rev = mint(1) / (*this)[i];FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);ret *= (*this)[i].pow(k);ret = (ret << (i * k)).pre(deg);if ((int)ret.size() < deg) ret.resize(deg, mint(0));return ret;}if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));}return FPS(deg, mint(0));}static void *ntt_ptr;static void set_fft();FPS &operator*=(const FPS &r);void ntt();void intt();void ntt_doubling();static int ntt_pr();FPS inv(int deg = -1) const;FPS exp(int deg = -1) const;};template <typename mint>void *FormalPowerSeries<mint>::ntt_ptr = nullptr;/*** @brief 多項式/形式的冪級数ライブラリ* @docs docs/fps/formal-power-series.md*/template <uint32_t mod>struct LazyMontgomeryModInt {using mint = LazyMontgomeryModInt;using i32 = int32_t;using u32 = uint32_t;using u64 = uint64_t;static constexpr u32 get_r() {u32 ret = mod;for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;return ret;}static constexpr u32 r = get_r();static constexpr u32 n2 = -u64(mod) % mod;static_assert(r * mod == 1, "invalid, r * mod != 1");static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");u32 a;constexpr LazyMontgomeryModInt() : a(0) {}constexpr LazyMontgomeryModInt(const int64_t &b): a(reduce(u64(b % mod + mod) * n2)){};static constexpr u32 reduce(const u64 &b) {return (b + u64(u32(b) * u32(-r)) * mod) >> 32;}constexpr mint &operator+=(const mint &b) {if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;return *this;}constexpr mint &operator-=(const mint &b) {if (i32(a -= b.a) < 0) a += 2 * mod;return *this;}constexpr mint &operator*=(const mint &b) {a = reduce(u64(a) * b.a);return *this;}constexpr mint &operator/=(const mint &b) {*this *= b.inverse();return *this;}constexpr mint operator+(const mint &b) const { return mint(*this) += b; }constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }constexpr bool operator==(const mint &b) const {return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);}constexpr bool operator!=(const mint &b) const {return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);}constexpr mint operator-() const { return mint() - mint(*this); }constexpr mint pow(u64 n) const {mint ret(1), mul(*this);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}constexpr mint inverse() const { return pow(mod - 2); }friend ostream &operator<<(ostream &os, const mint &b) {return os << b.get();}friend istream &operator>>(istream &is, mint &b) {int64_t t;is >> t;b = LazyMontgomeryModInt<mod>(t);return (is);}constexpr u32 get() const {u32 ret = reduce(a);return ret >= mod ? ret - mod : ret;}static constexpr u32 get_mod() { return mod; }};template <typename mint>struct NTT {static constexpr uint32_t get_pr() {uint32_t _mod = mint::get_mod();using u64 = uint64_t;u64 ds[32] = {};int idx = 0;u64 m = _mod - 1;for (u64 i = 2; i * i <= m; ++i) {if (m % i == 0) {ds[idx++] = i;while (m % i == 0) m /= i;}}if (m != 1) ds[idx++] = m;uint32_t _pr = 2;while (1) {int flg = 1;for (int i = 0; i < idx; ++i) {u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;while (b) {if (b & 1) r = r * a % _mod;a = a * a % _mod;b >>= 1;}if (r == 1) {flg = 0;break;}}if (flg == 1) break;++_pr;}return _pr;};static constexpr uint32_t mod = mint::get_mod();static constexpr uint32_t pr = get_pr();static constexpr int level = __builtin_ctzll(mod - 1);mint dw[level], dy[level];void setwy(int k) {mint w[level], y[level];w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));y[k - 1] = w[k - 1].inverse();for (int i = k - 2; i > 0; --i)w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];for (int i = 3; i < k; ++i) {dw[i] = dw[i - 1] * y[i - 2] * w[i];dy[i] = dy[i - 1] * w[i - 2] * y[i];}}NTT() { setwy(level); }void fft4(vector<mint> &a, int k) {if ((int)a.size() <= 1) return;if (k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}if (k & 1) {int v = 1 << (k - 1);for (int j = 0; j < v; ++j) {mint ajv = a[j + v];a[j + v] = a[j] - ajv;a[j] += ajv;}}int u = 1 << (2 + (k & 1));int v = 1 << (k - 2 - (k & 1));mint one = mint(1);mint imag = dw[1];while (v) {// jh = 0{int j0 = 0;int j1 = v;int j2 = j1 + v;int j3 = j2 + v;for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];mint t0p2 = t0 + t2, t1p3 = t1 + t3;mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;}}// jh >= 1mint ww = one, xx = one * dw[2], wx = one;for (int jh = 4; jh < u;) {ww = xx * xx, wx = ww * xx;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for (; j0 < je; ++j0, ++j2) {mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,t3 = a[j2 + v] * wx;mint t0p2 = t0 + t2, t1p3 = t1 + t3;mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;}xx *= dw[__builtin_ctzll((jh += 4))];}u <<= 2;v >>= 2;}}void ifft4(vector<mint> &a, int k) {if ((int)a.size() <= 1) return;if (k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}int u = 1 << (k - 2);int v = 1;mint one = mint(1);mint imag = dy[1];while (u) {// jh = 0{int j0 = 0;int j1 = v;int j2 = v + v;int j3 = j2 + v;for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;}}// jh >= 1mint ww = one, xx = one * dy[2], yy = one;u <<= 2;for (int jh = 4; jh < u;) {ww = xx * xx, yy = xx * imag;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for (; j0 < je; ++j0, ++j2) {mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;}xx *= dy[__builtin_ctzll(jh += 4)];}u >>= 4;v <<= 2;}if (k & 1) {u = 1 << (k - 1);for (int j = 0; j < u; ++j) {mint ajv = a[j] - a[j + u];a[j] += a[j + u];a[j + u] = ajv;}}}void ntt(vector<mint> &a) {if ((int)a.size() <= 1) return;fft4(a, __builtin_ctz(a.size()));}void intt(vector<mint> &a) {if ((int)a.size() <= 1) return;ifft4(a, __builtin_ctz(a.size()));mint iv = mint(a.size()).inverse();for (auto &x : a) x *= iv;}vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {int l = a.size() + b.size() - 1;if (min<int>(a.size(), b.size()) <= 40) {vector<mint> s(l);for (int i = 0; i < (int)a.size(); ++i)for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];return s;}int k = 2, M = 4;while (M < l) M <<= 1, ++k;setwy(k);vector<mint> s(M);for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];fft4(s, k);if (a.size() == b.size() && a == b) {for (int i = 0; i < M; ++i) s[i] *= s[i];} else {vector<mint> t(M);for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];fft4(t, k);for (int i = 0; i < M; ++i) s[i] *= t[i];}ifft4(s, k);s.resize(l);mint invm = mint(M).inverse();for (int i = 0; i < l; ++i) s[i] *= invm;return s;}void ntt_doubling(vector<mint> &a) {int M = (int)a.size();auto b = a;intt(b);mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;ntt(b);copy(begin(b), end(b), back_inserter(a));}};namespace ArbitraryNTT {using i64 = int64_t;using u128 = __uint128_t;constexpr int32_t m0 = 167772161;constexpr int32_t m1 = 469762049;constexpr int32_t m2 = 754974721;using mint0 = LazyMontgomeryModInt<m0>;using mint1 = LazyMontgomeryModInt<m1>;using mint2 = LazyMontgomeryModInt<m2>;constexpr int r01 = mint1(m0).inverse().get();constexpr int r02 = mint2(m0).inverse().get();constexpr int r12 = mint2(m1).inverse().get();constexpr int r02r12 = i64(r02) * r12 % m2;constexpr i64 w1 = m0;constexpr i64 w2 = i64(m0) * m1;template <typename T, typename submint>vector<submint> mul(const vector<T> &a, const vector<T> &b) {static NTT<submint> ntt;vector<submint> s(a.size()), t(b.size());for (int i = 0; i < (int)a.size(); ++i) s[i] = i64(a[i] % submint::get_mod());for (int i = 0; i < (int)b.size(); ++i) t[i] = i64(b[i] % submint::get_mod());return ntt.multiply(s, t);}template <typename T>vector<int> multiply(const vector<T> &s, const vector<T> &t, int mod) {auto d0 = mul<T, mint0>(s, t);auto d1 = mul<T, mint1>(s, t);auto d2 = mul<T, mint2>(s, t);int n = d0.size();vector<int> ret(n);const int W1 = w1 % mod;const int W2 = w2 % mod;for (int i = 0; i < n; i++) {int n1 = d1[i].get(), n2 = d2[i].get(), a = d0[i].get();int b = i64(n1 + m1 - a) * r01 % m1;int c = (i64(n2 + m2 - a) * r02r12 + i64(m2 - b) * r12) % m2;ret[i] = (i64(a) + i64(b) * W1 + i64(c) * W2) % mod;}return ret;}template <typename mint>vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {if (a.size() == 0 && b.size() == 0) return {};if (min<int>(a.size(), b.size()) < 128) {vector<mint> ret(a.size() + b.size() - 1);for (int i = 0; i < (int)a.size(); ++i)for (int j = 0; j < (int)b.size(); ++j) ret[i + j] += a[i] * b[j];return ret;}vector<int> s(a.size()), t(b.size());for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i].get();for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i].get();vector<int> u = multiply<int>(s, t, mint::get_mod());vector<mint> ret(u.size());for (int i = 0; i < (int)u.size(); ++i) ret[i] = mint(u[i]);return ret;}template <typename T>vector<u128> multiply_u128(const vector<T> &s, const vector<T> &t) {if (s.size() == 0 && t.size() == 0) return {};if (min<int>(s.size(), t.size()) < 128) {vector<u128> ret(s.size() + t.size() - 1);for (int i = 0; i < (int)s.size(); ++i)for (int j = 0; j < (int)t.size(); ++j) ret[i + j] += i64(s[i]) * t[j];return ret;}auto d0 = mul<T, mint0>(s, t);auto d1 = mul<T, mint1>(s, t);auto d2 = mul<T, mint2>(s, t);int n = d0.size();vector<u128> ret(n);for (int i = 0; i < n; i++) {i64 n1 = d1[i].get(), n2 = d2[i].get();i64 a = d0[i].get();i64 b = (n1 + m1 - a) * r01 % m1;i64 c = ((n2 + m2 - a) * r02r12 + (m2 - b) * r12) % m2;ret[i] = a + b * w1 + u128(c) * w2;}return ret;}} // namespace ArbitraryNTTtemplate <typename mint>void FormalPowerSeries<mint>::set_fft() {ntt_ptr = nullptr;}template <typename mint>void FormalPowerSeries<mint>::ntt() {exit(1);}template <typename mint>void FormalPowerSeries<mint>::intt() {exit(1);}template <typename mint>void FormalPowerSeries<mint>::ntt_doubling() {exit(1);}template <typename mint>int FormalPowerSeries<mint>::ntt_pr() {exit(1);}template <typename mint>FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(const FormalPowerSeries<mint>& r) {if (this->empty() || r.empty()) {this->clear();return *this;}auto ret = ArbitraryNTT::multiply(*this, r);return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {assert((*this)[0] != mint(0));if (deg == -1) deg = (*this).size();FormalPowerSeries<mint> ret({mint(1) / (*this)[0]});for (int i = 1; i < deg; i <<= 1)ret = (ret + ret - ret * ret * (*this).pre(i << 1)).pre(i << 1);return ret.pre(deg);}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {assert((*this).size() == 0 || (*this)[0] == mint(0));if (deg == -1) deg = (int)this->size();FormalPowerSeries<mint> ret({mint(1)});for (int i = 1; i < deg; i <<= 1) {ret = (ret * (pre(i << 1) + mint(1) - ret.log(i << 1))).pre(i << 1);}return ret.pre(deg);}using mint=LazyMontgomeryModInt<1000000007>;using fps=FormalPowerSeries<mint>;// combination mod prime// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619struct combination {vector<mint> fact, ifact;combination(int n):fact(n+1),ifact(n+1) {assert(n < MOD);fact[0] = 1;for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i;ifact[n] = fact[n].inverse();for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i;}mint operator()(int n, int k) {if (k < 0 || k > n) return 0;return fact[n]*ifact[k]*ifact[n-k];}mint p(int n,int k){return fact[n]*ifact[n-k];}} c(2000005);int main(){ios::sync_with_stdio(false);cin.tie(0);ll n,m,a,b;cin>>n>>m>>a>>b;fps v(m+1);rep(i,n){mint x=c(n-1,i);ll idx=(n-i-1)*a+i*(b+1);if(idx>=m)continue;if(i%2==0)v[idx+1]+=x;else v[idx+1]-=x;}fps u(m+1);rep(i,m+1){mint x=c(i+n-1,n-1);u[i]+=x;}for(ll i=0;i<=m-1;i++){u[i+1]+=u[i];}u=u.rev();mint ans=0;rep(i,m+1){mint x=v[i];x*=u[i];ans+=x;}cout<<ans<<endl;return 0;}