結果
問題 | No.1783 Remix Sum |
ユーザー | 👑 hos.lyric |
提出日時 | 2021-12-12 03:14:50 |
言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 1,590 ms / 10,000 ms |
コード長 | 15,950 bytes |
コンパイル時間 | 1,412 ms |
コンパイル使用メモリ | 117,204 KB |
実行使用メモリ | 30,628 KB |
最終ジャッジ日時 | 2024-07-20 12:06:55 |
合計ジャッジ時間 | 54,667 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge1 |
(要ログイン)
テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 13 ms
11,776 KB |
testcase_01 | AC | 13 ms
11,776 KB |
testcase_02 | AC | 13 ms
11,904 KB |
testcase_03 | AC | 13 ms
12,032 KB |
testcase_04 | AC | 53 ms
12,032 KB |
testcase_05 | AC | 52 ms
11,904 KB |
testcase_06 | AC | 195 ms
11,904 KB |
testcase_07 | AC | 1,318 ms
13,844 KB |
testcase_08 | AC | 348 ms
11,904 KB |
testcase_09 | AC | 346 ms
11,904 KB |
testcase_10 | AC | 53 ms
11,904 KB |
testcase_11 | AC | 53 ms
11,904 KB |
testcase_12 | AC | 1,298 ms
13,824 KB |
testcase_13 | AC | 1,306 ms
13,824 KB |
testcase_14 | AC | 344 ms
12,032 KB |
testcase_15 | AC | 1,576 ms
29,976 KB |
testcase_16 | AC | 1,460 ms
13,976 KB |
testcase_17 | AC | 1,462 ms
13,980 KB |
testcase_18 | AC | 57 ms
12,032 KB |
testcase_19 | AC | 345 ms
12,032 KB |
testcase_20 | AC | 510 ms
12,116 KB |
testcase_21 | AC | 341 ms
11,904 KB |
testcase_22 | AC | 332 ms
11,904 KB |
testcase_23 | AC | 376 ms
12,032 KB |
testcase_24 | AC | 482 ms
12,160 KB |
testcase_25 | AC | 200 ms
12,032 KB |
testcase_26 | AC | 1,330 ms
13,824 KB |
testcase_27 | AC | 190 ms
11,904 KB |
testcase_28 | AC | 197 ms
12,124 KB |
testcase_29 | AC | 516 ms
12,160 KB |
testcase_30 | AC | 500 ms
12,160 KB |
testcase_31 | AC | 357 ms
12,088 KB |
testcase_32 | AC | 1,549 ms
29,980 KB |
testcase_33 | AC | 494 ms
12,032 KB |
testcase_34 | AC | 504 ms
12,544 KB |
testcase_35 | AC | 1,326 ms
14,336 KB |
testcase_36 | AC | 1,590 ms
30,628 KB |
testcase_37 | AC | 1,588 ms
30,496 KB |
testcase_38 | AC | 1,341 ms
14,336 KB |
testcase_39 | AC | 523 ms
12,416 KB |
testcase_40 | AC | 214 ms
12,288 KB |
testcase_41 | AC | 532 ms
12,544 KB |
testcase_42 | AC | 530 ms
12,544 KB |
testcase_43 | AC | 1,341 ms
14,208 KB |
testcase_44 | AC | 93 ms
12,416 KB |
testcase_45 | AC | 209 ms
12,416 KB |
testcase_46 | AC | 366 ms
12,288 KB |
testcase_47 | AC | 509 ms
12,416 KB |
testcase_48 | AC | 1,330 ms
14,336 KB |
testcase_49 | AC | 1,562 ms
30,528 KB |
testcase_50 | AC | 93 ms
12,288 KB |
testcase_51 | AC | 208 ms
12,288 KB |
testcase_52 | AC | 368 ms
12,288 KB |
testcase_53 | AC | 512 ms
12,416 KB |
testcase_54 | AC | 1,304 ms
14,208 KB |
testcase_55 | AC | 1,567 ms
30,496 KB |
testcase_56 | AC | 103 ms
12,416 KB |
testcase_57 | AC | 211 ms
12,416 KB |
testcase_58 | AC | 359 ms
12,416 KB |
testcase_59 | AC | 505 ms
12,544 KB |
testcase_60 | AC | 1,188 ms
14,336 KB |
testcase_61 | AC | 1,572 ms
30,496 KB |
testcase_62 | AC | 95 ms
12,288 KB |
testcase_63 | AC | 210 ms
12,288 KB |
testcase_64 | AC | 366 ms
12,416 KB |
testcase_65 | AC | 512 ms
12,416 KB |
testcase_66 | AC | 1,326 ms
14,336 KB |
testcase_67 | AC | 34 ms
12,928 KB |
testcase_68 | AC | 64 ms
12,416 KB |
testcase_69 | AC | 205 ms
12,288 KB |
testcase_70 | AC | 356 ms
12,288 KB |
testcase_71 | AC | 506 ms
12,416 KB |
testcase_72 | AC | 1,326 ms
14,336 KB |
testcase_73 | AC | 1,207 ms
28,836 KB |
testcase_74 | AC | 65 ms
12,288 KB |
testcase_75 | AC | 203 ms
12,288 KB |
testcase_76 | AC | 361 ms
12,288 KB |
testcase_77 | AC | 505 ms
12,416 KB |
testcase_78 | AC | 1,307 ms
14,208 KB |
testcase_79 | AC | 733 ms
28,964 KB |
ソースコード
#include <cassert> #include <cmath> #include <cstdint> #include <cstdio> #include <cstdlib> #include <cstring> #include <algorithm> #include <bitset> #include <complex> #include <deque> #include <functional> #include <iostream> #include <map> #include <numeric> #include <queue> #include <set> #include <sstream> #include <string> #include <unordered_map> #include <unordered_set> #include <utility> #include <vector> using namespace std; using Int = long long; template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } //////////////////////////////////////////////////////////////////////////////// template <unsigned M_> struct ModInt { static constexpr unsigned M = M_; unsigned x; constexpr ModInt() : x(0U) {} constexpr ModInt(unsigned x_) : x(x_ % M) {} constexpr ModInt(unsigned long long x_) : x(x_ % M) {} constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {} constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {} ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; } ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; } ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; } ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); } ModInt pow(long long e) const { if (e < 0) return inv().pow(-e); ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b; } ModInt inv() const { unsigned a = M, b = x; int y = 0, z = 1; for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; } assert(a == 1U); return ModInt(y); } ModInt operator+() const { return *this; } ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; } ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); } ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); } ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); } ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); } template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); } template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); } template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); } template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); } explicit operator bool() const { return x; } bool operator==(const ModInt &a) const { return (x == a.x); } bool operator!=(const ModInt &a) const { return (x != a.x); } friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; } }; //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// // M: prime, G: primitive root, 2^K | M - 1 template <unsigned M_, unsigned G_, int K_> struct Fft { static_assert(2U <= M_, "Fft: 2 <= M must hold."); static_assert(M_ < 1U << 30, "Fft: M < 2^30 must hold."); static_assert(1 <= K_, "Fft: 1 <= K must hold."); static_assert(K_ < 30, "Fft: K < 30 must hold."); static_assert(!((M_ - 1U) & ((1U << K_) - 1U)), "Fft: 2^K | M - 1 must hold."); static constexpr unsigned M = M_; static constexpr unsigned M2 = 2U * M_; static constexpr unsigned G = G_; static constexpr int K = K_; ModInt<M> FFT_ROOTS[K + 1], INV_FFT_ROOTS[K + 1]; ModInt<M> FFT_RATIOS[K], INV_FFT_RATIOS[K]; Fft() { const ModInt<M> g(G); for (int k = 0; k <= K; ++k) { FFT_ROOTS[k] = g.pow((M - 1U) >> k); INV_FFT_ROOTS[k] = FFT_ROOTS[k].inv(); } for (int k = 0; k <= K - 2; ++k) { FFT_RATIOS[k] = -g.pow(3U * ((M - 1U) >> (k + 2))); INV_FFT_RATIOS[k] = FFT_RATIOS[k].inv(); } assert(FFT_ROOTS[1] == M - 1U); } // as[rev(i)] <- \sum_j \zeta^(ij) as[j] void fft(ModInt<M> *as, int n) const { assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << K); int m = n; if (m >>= 1) { for (int i = 0; i < m; ++i) { const unsigned x = as[i + m].x; // < M as[i + m].x = as[i].x + M - x; // < 2 M as[i].x += x; // < 2 M } } if (m >>= 1) { ModInt<M> prod = 1U; for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) { for (int i = i0; i < i0 + m; ++i) { const unsigned x = (prod * as[i + m]).x; // < M as[i + m].x = as[i].x + M - x; // < 3 M as[i].x += x; // < 3 M } prod *= FFT_RATIOS[__builtin_ctz(++h)]; } } for (; m; ) { if (m >>= 1) { ModInt<M> prod = 1U; for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) { for (int i = i0; i < i0 + m; ++i) { const unsigned x = (prod * as[i + m]).x; // < M as[i + m].x = as[i].x + M - x; // < 4 M as[i].x += x; // < 4 M } prod *= FFT_RATIOS[__builtin_ctz(++h)]; } } if (m >>= 1) { ModInt<M> prod = 1U; for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) { for (int i = i0; i < i0 + m; ++i) { const unsigned x = (prod * as[i + m]).x; // < M as[i].x = (as[i].x >= M2) ? (as[i].x - M2) : as[i].x; // < 2 M as[i + m].x = as[i].x + M - x; // < 3 M as[i].x += x; // < 3 M } prod *= FFT_RATIOS[__builtin_ctz(++h)]; } } } for (int i = 0; i < n; ++i) { as[i].x = (as[i].x >= M2) ? (as[i].x - M2) : as[i].x; // < 2 M as[i].x = (as[i].x >= M) ? (as[i].x - M) : as[i].x; // < M } } // as[i] <- (1/n) \sum_j \zeta^(-ij) as[rev(j)] void invFft(ModInt<M> *as, int n) const { assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << K); int m = 1; if (m < n >> 1) { ModInt<M> prod = 1U; for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) { for (int i = i0; i < i0 + m; ++i) { const unsigned long long y = as[i].x + M - as[i + m].x; // < 2 M as[i].x += as[i + m].x; // < 2 M as[i + m].x = (prod.x * y) % M; // < M } prod *= INV_FFT_RATIOS[__builtin_ctz(++h)]; } m <<= 1; } for (; m < n >> 1; m <<= 1) { ModInt<M> prod = 1U; for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) { for (int i = i0; i < i0 + (m >> 1); ++i) { const unsigned long long y = as[i].x + M2 - as[i + m].x; // < 4 M as[i].x += as[i + m].x; // < 4 M as[i].x = (as[i].x >= M2) ? (as[i].x - M2) : as[i].x; // < 2 M as[i + m].x = (prod.x * y) % M; // < M } for (int i = i0 + (m >> 1); i < i0 + m; ++i) { const unsigned long long y = as[i].x + M - as[i + m].x; // < 2 M as[i].x += as[i + m].x; // < 2 M as[i + m].x = (prod.x * y) % M; // < M } prod *= INV_FFT_RATIOS[__builtin_ctz(++h)]; } } if (m < n) { for (int i = 0; i < m; ++i) { const unsigned y = as[i].x + M2 - as[i + m].x; // < 4 M as[i].x += as[i + m].x; // < 4 M as[i + m].x = y; // < 4 M } } const ModInt<M> invN = ModInt<M>(n).inv(); for (int i = 0; i < n; ++i) { as[i] *= invN; } } void fft(vector<ModInt<M>> &as) const { fft(as.data(), as.size()); } void invFft(vector<ModInt<M>> &as) const { invFft(as.data(), as.size()); } vector<ModInt<M>> convolve(vector<ModInt<M>> as, vector<ModInt<M>> bs) const { if (as.empty() || bs.empty()) return {}; const int len = as.size() + bs.size() - 1; int n = 1; for (; n < len; n <<= 1) {} as.resize(n); fft(as); bs.resize(n); fft(bs); for (int i = 0; i < n; ++i) as[i] *= bs[i]; invFft(as); as.resize(len); return as; } vector<ModInt<M>> square(vector<ModInt<M>> as) const { if (as.empty()) return {}; const int len = as.size() + as.size() - 1; int n = 1; for (; n < len; n <<= 1) {} as.resize(n); fft(as); for (int i = 0; i < n; ++i) as[i] *= as[i]; invFft(as); as.resize(len); return as; } }; constexpr unsigned MO = 120586241; using Mint = ModInt<MO>; const Fft<MO, 6, 20> FFT; constexpr Mint G = 9142366; constexpr int LIM = 1 << 19; Mint inv[LIM], fac[LIM], invFac[LIM]; void prepare() { inv[1] = 1; for (int i = 2; i < LIM; ++i) { inv[i] = -((Mint::M / i) * inv[Mint::M % i]); } fac[0] = invFac[0] = 1; for (int i = 1; i < LIM; ++i) { fac[i] = fac[i - 1] * i; invFac[i] = invFac[i - 1] * inv[i]; } } Mint binom(Int n, Int k) { if (n < 0) { if (k >= 0) { return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k); } else if (n - k >= 0) { return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k); } else { return 0; } } else { if (0 <= k && k <= n) { assert(n < LIM); return fac[n] * invFac[k] * invFac[n - k]; } else { return 0; } } } constexpr int TEN[] = { 1, 10, 100, 1000, 10000, 100000, }; int N, K, T; Int M; vector<int> A; constexpr int MAX_LEN = 1 << 19; int zw[MAX_LEN]; Mint zas[5][MAX_LEN], zbs[5][MAX_LEN], zcs[5][MAX_LEN]; vector<Mint> multiMul(const vector<Mint> &as, const vector<Mint> &bs, int na = -1, int nb = -1) { if (!~na) na = as.size(); if (!~nb) nb = bs.size(); chmin(na, TEN[T]); chmin(nb, TEN[T]); assert((int)as.size() >= na); assert((int)bs.size() >= nb); const int nc = min(na + nb, TEN[T]); int len = 1; for (; len < na + nb; len <<= 1) {} for (int t = 0; t < T; ++t) { fill(zas[t], zas[t] + len, 0); fill(zbs[t], zbs[t] + len, 0); fill(zcs[t], zcs[t] + len, 0); } for (int h = 0; h < na; ++h) { zas[zw[h]][h] += as[h]; } for (int h = 0; h < nb; ++h) { zbs[zw[h]][h] += bs[h]; } for (int t = 0; t < T; ++t) { FFT.fft(zas[t], len); FFT.fft(zbs[t], len); } for (int ta = 0; ta < T; ++ta) for (int tb = 0; tb < T; ++tb) { const int t = (ta + tb) % T; for (int h = 0; h < len; ++h) { zcs[t][h] += zas[ta][h] * zbs[tb][h]; } } for (int t = 0; t < T; ++t) { FFT.invFft(zcs[t], len); } vector<Mint> cs(nc, 0); for (int h = 0; h < nc; ++h) { cs[h] = zcs[zw[h]][h]; } return cs; } // TODO: save FFT... // b <- b - (a b - 1) b vector<Mint> multiInv(const vector<Mint> &as, int n) { vector<Mint> bs(n, 0); bs[0] = 1; for (int m = 1; m < n; m <<= 1) { auto cs = multiMul(as, bs, m << 1, m); cs[0] -= 1; cs = multiMul(cs, bs, -1, m); for (int h = m; h < m << 1 && h < n; ++h) bs[h] -= cs[h]; } return bs; } // D log(a) = (D a) / a vector<Mint> multiLog(const vector<Mint> &as, int n) { chmin(n, TEN[T]); assert((int)as.size() >= n); assert(as[0] == 1); vector<Mint> bs(n, 0); for (int h = 0; h < n; ++h) bs[h] = h * as[h]; bs = multiMul(bs, multiInv(as, n)); for (int h = 1; h < n; ++h) bs[h] *= inv[h]; return bs; } // b <- b - (I (c (D b - b D (a mod x^m)) + D (a mod x^m)) - a) b // c <- c - (b c - 1) c vector<Mint> multiExp(const vector<Mint> &as, int n) { // cerr<<" multiExp n = "<<n<<", as = ";pv(as.begin(),as.end()); chmin(n, TEN[T]); assert((int)as.size() >= n); assert(as[0] == 0); vector<Mint> Das(n); for (int h = 0; h < n; ++h) { Das[h] = h * as[h]; } vector<Mint> bs(n, 0), cs(n, 0); bs[0] = cs[0] = 1; for (int m = 1; m < n; m <<= 1) { vector<Mint> Dbs(m); for (int h = 0; h < m; ++h) Dbs[h] = h * bs[h]; auto ds = multiMul(bs, Das, m, m); for (int h = 0; h < (int)ds.size(); ++h) ds[h] *= -1; for (int h = 0; h < m; ++h) ds[h] += Dbs[h]; ds = multiMul(cs, ds, m, -1); for (int h = 0; h < m; ++h) ds[h] += Das[h]; for (int h = 0; h < (int)ds.size(); ++h) ds[h] *= inv[h]; for (int h = 0; h < m << 1 && h < n; ++h) ds[h] -= as[h]; ds = multiMul(ds, bs, -1, m); for (int h = m; h < m << 1 && h < n; ++h) bs[h] -= ds[h]; ds = multiMul(bs, cs, m << 1, m); ds[0] -= 1; ds = multiMul(ds, cs, -1, m); for (int h = m; h < m << 1 && h < n; ++h) cs[h] -= ds[h]; } // cerr<<" multiExp bs = ";pv(bs.begin(),bs.end()); // cerr<<" multiExp cs = ";pv(cs.begin(),cs.end()); return bs; } vector<Mint> multiPow(vector<Mint> as, Int e) { // cerr<<"multiPow e = "<<e<<", as = ";pv(as.begin(),as.end()); if (T == 0) { return {as[0].pow(e)}; } else { if (as[0]) { const Mint a0e = as[0].pow(e); const Mint invA0 = as[0].inv(); for (int h = 0; h < TEN[T]; ++h) { as[h] *= invA0; } as = multiLog(as, TEN[T]); for (int h = 0; h < TEN[T]; ++h) { as[h] *= e; } as = multiExp(as, TEN[T]); for (int h = 0; h < TEN[T]; ++h) { as[h] *= a0e; } // cerr<<"multiPow return ";pv(as.begin(),as.end()); return as; } else { if (e >= T * (10 - 1)) { return vector<Mint>(TEN[T], 0); } vector<Mint> bs(TEN[T], 0); bs[0] = 1; for (; e; e >>= 1) { if (e & 1) bs = multiMul(bs, as); as = multiMul(as, as); } return bs; } } } Mint GG[10][10], invGG[10][10]; void dft(vector<Mint> &as) { Mint work0[10], work1[10]; for (int k = T; k < K; ++k) { for (int h = 0; h < TEN[K]; ++h) if (h / TEN[k] % 10 == 0) { for (int i = 0; i < 10; ++i) { work0[i] = as[h + TEN[k] * i]; } for (int i = 0; i < 10; ++i) { work1[i] = 0; for (int j = 0; j < 10; ++j) { work1[i] += GG[i][j] * work0[j]; } } for (int i = 0; i < 10; ++i) { as[h + TEN[k] * i] = work1[i]; } } } } void invDft(vector<Mint> &as) { Mint work0[10], work1[10]; for (int k = T; k < K; ++k) { for (int h = 0; h < TEN[K]; ++h) if (h / TEN[k] % 10 == 0) { for (int i = 0; i < 10; ++i) { work0[i] = as[h + TEN[k] * i]; } for (int i = 0; i < 10; ++i) { work1[i] = 0; for (int j = 0; j < 10; ++j) { work1[i] += invGG[i][j] * work0[j]; } } for (int i = 0; i < 10; ++i) { as[h + TEN[k] * i] = work1[i]; } } } const Mint c = Mint(TEN[K - T]).inv(); for (int h = 0; h < TEN[K]; ++h) { as[h] *= c; } } int main() { prepare(); // cerr<<G.pow(2)<<" "<<G.pow(5)<<" "<<G.pow(10)<<endl; for (int i = 0; i < 10; ++i) for (int j = 0; j < 10; ++j) { GG[i][j] = G.pow(i * j); invGG[i][j] = GG[i][j].inv(); } for (; ~scanf("%d%d%lld%d", &N, &K, &M, &T); ) { A.resize(N); for (int i = 0; i < N; ++i) { scanf("%d", &A[i]); } memset(zw, 0, sizeof(zw)); for (int h = 0; h < TEN[T]; ++h) { for (int t = 1; t < T; ++t) { zw[h] += h / TEN[t]; } zw[h] %= max(T, 1); } // cerr<<"zw = ";pv(zw,zw+TEN[T]); vector<Mint> fs(TEN[K], 0); for (int i = 0; i < N; ++i) { fs[A[i]] += 1; } dft(fs); for (int h0 = 0; h0 < TEN[K]; h0 += TEN[T]) { const auto res = multiPow(vector<Mint>(fs.begin() + h0, fs.begin() + h0 + TEN[T]), M); for (int i = 0; i < TEN[T]; ++i) { fs[h0 + i] = res[i]; } } invDft(fs); for (int h = 0; h < TEN[K]; ++h) { printf("%u\n", fs[h].x); } #ifdef LOCAL cout<<"===="<<endl; #endif if(T==2){ vector<Mint>waf(100,0); waf[1]=1; waf[10]=2; multiExp(waf,100); } } return 0; }