結果
問題 | No.2396 等差二項展開 |
ユーザー |
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提出日時 | 2023-08-03 01:23:56 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 26 ms / 6,000 ms |
コード長 | 20,971 bytes |
コンパイル時間 | 2,822 ms |
コンパイル使用メモリ | 230,596 KB |
最終ジャッジ日時 | 2025-02-15 21:38:08 |
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 |
---|---|
other | AC * 31 |
ソースコード
#line 1 "main.cpp"//#pragma GCC target("avx,avx2")//#pragma GCC optimize("O3")//#pragma GCC optimize("unroll-loops")#include<bits/stdc++.h>#ifdef LOCAL#include <debug.hpp>#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)#else#define debug(...) (static_cast<void>(0))#endifusing namespace std;using ll = long long;using ld = long double;using pll = pair<ll, ll>;using pii = pair<int, int>;using vi = vector<int>;using vvi = vector<vi>;using vvvi = vector<vvi>;using vl = vector<ll>;using vvl = vector<vl>;using vvvl = vector<vvl>;using vpii = vector<pii>;using vpll = vector<pll>;using vs = vector<string>;template<class T> using pq = priority_queue<T, vector<T>, greater<T>>;#define overload4(_1, _2, _3, _4, name, ...) name#define overload3(a,b,c,name,...) name#define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER)#define rep2(i, n) for (ll i = 0; i < (n); ++i)#define rep3(i, a, b) for (ll i = (a); i < (b); ++i)#define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c))#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)#define rrep1(n) for(ll i = (n) - 1;i >= 0;i--)#define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--)#define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--)#define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c)#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)#define all1(i) begin(i) , end(i)#define all2(i,a) begin(i) , begin(i) + a#define all3(i,a,b) begin(i) + a , begin(i) + b#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)#define sum(...) accumulate(all(__VA_ARGS__),0LL)template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; }template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; }template<class T> auto min(const T& a){return *min_element(all(a));}template<class T> auto max(const T& a){return *max_element(all(a));}template<class... Ts> void in(Ts&... t);#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)#define VEC(type, name, size) vector<type> name(size); in(name)#define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name)ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;}ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }ll GCD(ll a,ll b) { if(a == 0 || b == 0) return 0; if(a % b == 0) return b; else return GCD(b,a%b);}ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;}namespace IO{#define VOID(a) decltype(void(a))struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(12);}} setting;template<int I> struct P : P<I-1>{};template<> struct P<0>{};template<class T> void i(T& t){ i(t, P<3>{}); }void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; }template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; }template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); }template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){in(get<idx>(t)...);}template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){ituple(t, make_index_sequence<tuple_size<T>::value>{});}#undef VOID}#define unpack(a) (void)initializer_list<int>{(a, 0)...}template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); }#undef unpackstatic const double PI = 3.1415926535897932;template <class F> struct REC {F f;REC(F &&f_) : f(forward<F>(f_)) {}template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }};constexpr int mod = 1000000007;//constexpr int mod = 998244353;#line 2 "library/modint/barrett-reduction.hpp"struct Barrett {using u32 = unsigned int;using i64 = long long;using u64 = unsigned long long;u32 m;u64 im;Barrett() : m(), im() {}Barrett(int n) : m(n), im(u64(-1) / m + 1) {}constexpr inline i64 quo(u64 n) {u64 x = u64((__uint128_t(n) * im) >> 64);u32 r = n - x * m;return m <= r ? x - 1 : x;}constexpr inline i64 rem(u64 n) {u64 x = u64((__uint128_t(n) * im) >> 64);u32 r = n - x * m;return m <= r ? r + m : r;}constexpr inline pair<i64, int> quorem(u64 n) {u64 x = u64((__uint128_t(n) * im) >> 64);u32 r = n - x * m;if (m <= r) return {x - 1, r + m};return {x, r};}constexpr inline i64 pow(u64 n, i64 p) {u32 a = rem(n), r = m == 1 ? 0 : 1;while (p) {if (p & 1) r = rem(u64(r) * a);a = rem(u64(a) * a);p >>= 1;}return r;}};#line 3 "library/modint/ArbitaryModint.hpp"struct ArbitraryModint {int x;ArbitraryModint():x(0) {}ArbitraryModint(int64_t y) {int z = y % get_mod();if(z < 0) z += get_mod();x = z;}ArbitraryModint &operator+=(const ArbitraryModint &p) {if((x += p.x) >= get_mod()) x -= get_mod();return *this;}ArbitraryModint &operator-=(const ArbitraryModint &p) {if((x += get_mod() - p.x) >= get_mod()) x -= get_mod();return *this;}ArbitraryModint &operator*=(const ArbitraryModint &p) {x = rem((unsigned long long)x * p.x);return *this;}ArbitraryModint &operator/=(const ArbitraryModint &p) {*this *= p.inverse();return *this;}ArbitraryModint operator-() const {return ArbitraryModint(-x);};ArbitraryModint operator+(const ArbitraryModint &p) const{return ArbitraryModint(*this) += p;}ArbitraryModint operator-(const ArbitraryModint &p) const{return ArbitraryModint(*this) -= p;}ArbitraryModint operator*(const ArbitraryModint &p) const{return ArbitraryModint(*this) *= p;}ArbitraryModint operator/(const ArbitraryModint &p) const {return ArbitraryModint(*this) /= p;}bool operator==(const ArbitraryModint &p) {return x == p.x;}bool operator!=(const ArbitraryModint &p) {return x != p.x;}ArbitraryModint inverse() const {int a = x,b = get_mod(),u = 1,v = 0,t;while(b > 0) {t = a / b;swap(a -= t * b,b);swap(u -= t * v,v);}return ArbitraryModint(u);}ArbitraryModint pow(int64_t n) const {ArbitraryModint ret(1),mul(x);while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os,const ArbitraryModint &p) {return os << p.x;}friend istream &operator>>(istream &is,ArbitraryModint &a) {int64_t t;is >> t;a = ArbitraryModint(t);return (is);}int get() const {return x;}inline unsigned int rem(unsigned long long p) {return barrett().rem(p);};static inline Barrett &barrett() {static Barrett b;return b;}static inline int &get_mod() {static int mod = 0;return mod;}static void set_mod(int md) {assert(0 < md && md <= (1LL << 30) - 1);get_mod() = md;barrett() = Barrett(md);}};#line 85 "main.cpp"using mint = ArbitraryModint;using vm = vector<mint>;using vvm = vector<vm>;using vvvm = vector<vvm>;#line 2 "library/modint/LazyMontgomeryModint.hpp"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);static_assert(mod < (1 << 30));static_assert((mod & 1) == 1);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; }};#line 2 "library/ntt/ntt.hpp"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) {{int j0 = 0,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;}}mint 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) {{int j0 = 0,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 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;}}mint 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), t(M);for(int i = 0;i < (int)a.size();++i) s[i] = a[i];for(int i = 0;i < (int)b.size();++i) t[i] = b[i];fft4(s,k);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));}};#line 4 "library/ntt/ArbitraryNTT.hpp"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 ArbitraryNTT#line 90 "main.cpp"int main() {LL(n,m);INT(l,k,b);mint::set_mod(b);vm f = {1,1};vm g = {1};rep(i,60) {if(n >> i & 1) {g = ArbitraryNTT::multiply(f,g);rrep(i,l,g.size()) {g[i - l] += g[i] * m;}if(g.size() > l) g.resize(l);}f = ArbitraryNTT::multiply(f,f);rrep(i,l,f.size()) {f[i - l] += f[i] * m;}if(f.size() > l) f.resize(l);}debug(g);cout << g[k] << '\n';}