結果
| 問題 | No.1025 Modular Equation |
| ユーザー |
 ei1333333
|
| 提出日時 | 2020-04-10 23:29:58 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 14,074 bytes |
| コンパイル時間 | 3,706 ms |
| コンパイル使用メモリ | 224,412 KB |
| 最終ジャッジ日時 | 2025-01-09 17:01:35 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 6 WA * 1 TLE * 25 |
ソースコード
#include<bits/stdc++.h>using namespace std;using int64 = long long;const int mod = 1e9 + 7;// const int mod = 998244353;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 {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)};}template< typename T >T mod_pow(T x, T n, const T &p) {T ret = 1;while(n > 0) {if(n & 1) (ret *= x) %= p;(x *= x) %= p;n >>= 1;}return ret;}static constexpr uint32_t get_r(int mod) {uint64_t ret = 1, m = mod, n = mod - 2;while(n) {ret = uint32_t(ret * m);m = uint32_t(m * m);n >>= 1;}return ret;};template< uint32_t mod >struct LazyMontgomeryModInt {using mint = LazyMontgomeryModInt;using i32 = int32_t;using u32 = uint32_t;using u64 = uint64_t;static constexpr u32 r = get_r(mod);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;LazyMontgomeryModInt() : a(0) {}LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)) {};static u32 reduce(const u64 &b) {return u32(b >> 32) + mod - u32((u64(u32(b) * r) * mod) >> 32);}mint &operator+=(const mint &b) {if(i32(a += b.a - 2 * mod) < 0) a += 2 * mod;return *this;}mint &operator-=(const mint &b) {if(i32(a -= b.a) < 0) a += 2 * mod;return *this;}mint &operator*=(const mint &b) {a = reduce(u64(a) * b.a);return *this;}mint &operator/=(const mint &b) {*this *= b.inverse();return *this;}mint operator+(const mint &b) const { return mint(*this) += b; }mint operator-(const mint &b) const { return mint(*this) -= b; }mint operator*(const mint &b) const { return mint(*this) *= b; }mint operator/(const mint &b) const { return mint(*this) /= b; }u32 get() const {u32 ret = reduce(a);return ret >= mod ? ret - mod : ret;}mint pow(u64 n) const {mint ret(1), mul(*this);while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}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);}mint inverse() const { return pow(mod - 2); }static constexpr u32 get_mod() { return mod; }};static constexpr uint32_t get_pr(uint32_t 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;};template< typename mint >struct NTT {static constexpr uint32_t mod = mint::get_mod();static constexpr uint32_t pr = get_pr(mod);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];}}void fft4(vector< mint > &a, int k) {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) {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;}}}vector< mint > multiply(const vector< mint > &a, const vector< mint > &b) {int l = a.size() + b.size() - 1;int k = 2, M = 4;while(M < l) M <<= 1, ++k;#ifdef NyaanDebugassert(k <= level);#endifsetwy(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;}};// LazyMontgomeryModInt専用。2^24まで可能namespace ArbitaryNTT {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 >;// modint用template< typename submint, typename mint >vector< submint > mul(const vector< mint > &a, const vector< mint > &b) {int l = a.size() + b.size() - 1;int k = 2, M = 4;while(M < l) M <<= 1, ++k;NTT< submint > ntt;vector< submint > s(M), t(M);for(int i = 0; i < (int) a.size(); ++i) {s[i].a = submint::reduce(uint64_t(a[i].a) * submint::n2);}for(int i = 0; i < (int) b.size(); ++i) {t[i].a = submint::reduce(uint64_t(b[i].a) * submint::n2);}ntt.setwy(k);ntt.fft4(s, k);ntt.fft4(t, k);for(int i = 0; i < M; ++i) s[i] *= t[i];ntt.ifft4(s, k);s.resize(l);submint invm = submint(M).inverse();for(int i = 0; i < l; ++i) s[i] *= invm;return s;}template< typename mint >vector< mint > multiply(const vector< mint > &s, const vector< mint > &t) {auto d0 = mul< mint0 >(s, t);auto d1 = mul< mint1 >(s, t);auto d2 = mul< mint2 >(s, t);int n = d0.size();vector< mint > res(n);using i64 = int64_t;static const int r01 = mint1(m0).inverse().get();static const int r02 = mint2(m0).inverse().get();static const int r12 = mint2(m1).inverse().get();static const int r02r12 = i64(r02) * r12 % m2;static const int w1 = m0 % mint::get_mod();static const int w2 = i64(w1) * m1 % mint::get_mod();// reduceに代入出来る数はmod * 2^32未満。一方、// a + b * w1 + c * w2// <= (m0-1) + (m1-1)*(mod-1) + (m2-1)*(mod-1)// = (m0-1) + (m1+m2-2)*(mod-1)// < 2^32+2^32*(mod-1) = 2^32*mod// が導かれるので、for文内部の5行目でmodを取らなくて良いとわかる。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;res[i].a = mint::reduce(a + b * w1 + c * w2);}return res;}// int用template< typename submint, int mod >vector< submint > int_friendly_mul(const vector< int > &a, const vector< int > &b) {int l = a.size() + b.size() - 1;int k = 2, M = 4;while(M < l) M <<= 1, ++k;NTT< submint > ntt;vector< submint > s(M), t(M);for(int i = 0; i < (int) a.size(); ++i) {s[i].a = submint::reduce(uint64_t(a[i]) * submint::n2);}for(int i = 0; i < (int) b.size(); ++i) {t[i].a = submint::reduce(uint64_t(b[i]) * submint::n2);}ntt.setwy(k);ntt.fft4(s, k);ntt.fft4(t, k);for(int i = 0; i < M; ++i) s[i] = s[i] * t[i];ntt.ifft4(s, k);s.resize(l);submint invm = submint(M).inverse();for(int i = 0; i < l; ++i) s[i] *= invm;return s;}template< int mod >vector< int > int_friendly_multiply(const vector< int > &s, const vector< int > &t) {auto d0 = int_friendly_mul< mint0, mod >(s, t);auto d1 = int_friendly_mul< mint1, mod >(s, t);auto d2 = int_friendly_mul< mint2, mod >(s, t);int n = d0.size();vector< int > res(n);using i64 = int64_t;static const int r01 = mint1(m0).inverse().get();static const int r02 = mint2(m0).inverse().get();static const int r12 = mint2(m1).inverse().get();static const int r02r12 = i64(r02) * r12 % m2;static const int w1 = m0 % mod;static const int w2 = i64(w1) * m1 % mod;// reduceに代入出来る数はmod * 2^32未満。一方、// a + b * w1 + c * w2// <= (m0-1) + (m1-1)*(mod-1) + (m2-1)*(mod-1)// = (m0-1) + (m1+m2-2)*(mod-1)// < 2^32+2^32*(mod-1) = 2^32*mod// が導かれるので、for文内部の5行目でmodを取らなくて良いとわかる。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;res[i] = (a + b * w1 + c * w2) % mod;}return res;}}int main() {int P, N, K, B;cin >> P >> N >> K >> B;vector< int64 > A(N);cin >> A;vector< int64 > beet(P);for(int i = 0; i < P; i++) {beet[mod_pow< int64 >(i, K, P)]++;}constexpr uint32_t MOD = 1000000007;using mint = LazyMontgomeryModInt< MOD >;auto dp = make_v< mint >(P);dp[0] = 1;for(int i = 0; i < N; i++) {vector< int > shift(P);for(int k = 0; k < P; k++) shift[k] = 1LL * A[i] * k % P;vector< mint > dp3(P);for(int k = 0; k < P; k++) dp3[shift[k]] = beet[k];auto dp2 = ArbitaryNTT::multiply(dp, dp3);for(int k = 0; k < dp.size(); k++) dp[k] = 0;for(int k = 0; k < dp2.size(); k++) dp[k % P] += dp2[k];}cout << dp[B].get() << endl;}