結果
問題 | No.1783 Remix Sum |
ユーザー | 👑 hos.lyric |
提出日時 | 2021-12-12 01:11:02 |
言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 5,213 ms / 10,000 ms |
コード長 | 13,031 bytes |
コンパイル時間 | 2,325 ms |
コンパイル使用メモリ | 136,900 KB |
実行使用メモリ | 16,512 KB |
最終ジャッジ日時 | 2023-09-27 15:29:23 |
合計ジャッジ時間 | 65,073 ms |
ジャッジサーバーID (参考情報) |
judge15 / judge13 |
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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 | 2 ms
5,592 KB |
testcase_01 | AC | 1 ms
4,380 KB |
testcase_02 | AC | 2 ms
4,380 KB |
testcase_03 | AC | 2 ms
5,592 KB |
testcase_04 | AC | 37 ms
4,384 KB |
testcase_05 | AC | 35 ms
4,376 KB |
testcase_06 | AC | 103 ms
5,736 KB |
testcase_07 | AC | 493 ms
12,388 KB |
testcase_08 | AC | 141 ms
7,692 KB |
testcase_09 | AC | 139 ms
7,664 KB |
testcase_10 | AC | 36 ms
4,376 KB |
testcase_11 | AC | 36 ms
4,380 KB |
testcase_12 | AC | 573 ms
12,136 KB |
testcase_13 | AC | 293 ms
12,208 KB |
testcase_14 | AC | 117 ms
7,664 KB |
testcase_15 | AC | 476 ms
16,056 KB |
testcase_16 | AC | 484 ms
12,152 KB |
testcase_17 | AC | 573 ms
12,216 KB |
testcase_18 | AC | 38 ms
4,376 KB |
testcase_19 | AC | 164 ms
7,660 KB |
testcase_20 | AC | 197 ms
9,732 KB |
testcase_21 | AC | 166 ms
7,796 KB |
testcase_22 | AC | 166 ms
7,932 KB |
testcase_23 | AC | 226 ms
9,724 KB |
testcase_24 | AC | 119 ms
9,720 KB |
testcase_25 | AC | 104 ms
5,620 KB |
testcase_26 | AC | 573 ms
12,280 KB |
testcase_27 | AC | 105 ms
5,700 KB |
testcase_28 | AC | 77 ms
5,672 KB |
testcase_29 | AC | 192 ms
9,740 KB |
testcase_30 | AC | 195 ms
9,764 KB |
testcase_31 | AC | 160 ms
7,796 KB |
testcase_32 | AC | 697 ms
16,036 KB |
testcase_33 | AC | 191 ms
9,724 KB |
testcase_34 | AC | 136 ms
10,116 KB |
testcase_35 | AC | 301 ms
12,528 KB |
testcase_36 | AC | 371 ms
16,400 KB |
testcase_37 | AC | 354 ms
16,268 KB |
testcase_38 | AC | 304 ms
12,584 KB |
testcase_39 | AC | 133 ms
10,028 KB |
testcase_40 | AC | 74 ms
6,016 KB |
testcase_41 | AC | 131 ms
10,028 KB |
testcase_42 | AC | 133 ms
10,004 KB |
testcase_43 | AC | 308 ms
12,652 KB |
testcase_44 | AC | 80 ms
4,376 KB |
testcase_45 | AC | 568 ms
5,896 KB |
testcase_46 | AC | 1,024 ms
7,980 KB |
testcase_47 | AC | 1,496 ms
9,940 KB |
testcase_48 | AC | 4,067 ms
12,652 KB |
testcase_49 | AC | 5,213 ms
16,368 KB |
testcase_50 | AC | 79 ms
4,380 KB |
testcase_51 | AC | 587 ms
5,972 KB |
testcase_52 | AC | 1,044 ms
8,064 KB |
testcase_53 | AC | 1,524 ms
10,008 KB |
testcase_54 | AC | 4,084 ms
12,476 KB |
testcase_55 | AC | 4,933 ms
16,344 KB |
testcase_56 | AC | 83 ms
4,380 KB |
testcase_57 | AC | 562 ms
6,012 KB |
testcase_58 | AC | 1,022 ms
7,944 KB |
testcase_59 | AC | 1,487 ms
9,980 KB |
testcase_60 | AC | 3,547 ms
12,612 KB |
testcase_61 | AC | 4,909 ms
16,388 KB |
testcase_62 | AC | 79 ms
4,380 KB |
testcase_63 | AC | 563 ms
5,888 KB |
testcase_64 | AC | 1,019 ms
8,068 KB |
testcase_65 | AC | 1,495 ms
10,280 KB |
testcase_66 | AC | 4,031 ms
12,580 KB |
testcase_67 | AC | 20 ms
5,812 KB |
testcase_68 | AC | 50 ms
4,380 KB |
testcase_69 | AC | 163 ms
5,888 KB |
testcase_70 | AC | 265 ms
7,944 KB |
testcase_71 | AC | 378 ms
10,064 KB |
testcase_72 | AC | 947 ms
12,524 KB |
testcase_73 | AC | 1,203 ms
16,512 KB |
testcase_74 | AC | 52 ms
4,380 KB |
testcase_75 | AC | 170 ms
6,012 KB |
testcase_76 | AC | 276 ms
7,940 KB |
testcase_77 | AC | 196 ms
10,008 KB |
testcase_78 | AC | 668 ms
12,584 KB |
testcase_79 | AC | 691 ms
16,276 KB |
ソースコード
#pragma GCC optimize ("Ofast") #pragma GCC optimize ("unroll-loops") #pragma GCC target ("avx") #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 TEN[] = { 1, 10, 100, 1000, 10000, 100000, }; int N, K, T; Int M; vector<int> A; 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 len; int zw[1 << 18]; vector<Mint> ei(const vector<Mint> &as, const vector<Mint> &bs) { // cerr<<" ei"<<endl; // cerr<<" as = ";pv(as.begin(),as.end()); // cerr<<" bs = ";pv(bs.begin(),bs.end()); static Mint f[5][1 << 18], g[5][1 << 18]; for (int t = 0; t < T; ++t) { fill(f[t], f[t] + len, 0); fill(g[t], g[t] + len, 0); } for (int h = 0; h < TEN[T]; ++h) { f[zw[h]][h] += as[h]; g[zw[h]][h] += bs[h]; } for (int t = 0; t < T; ++t) { // cerr<<" f["<<t<<"] = ";pv(f[t],f[t]+len); // cerr<<" g["<<t<<"] = ";pv(g[t],g[t]+len); FFT.fft(f[t], len); FFT.fft(g[t], len); } Mint work[10]; for (int h = 0; h < len; ++h) { fill(work, work + 2 * T, 0); for (int t = 0; t < T; ++t) for (int tt = 0; tt < T; ++tt) { work[t + tt] += f[t][h] * g[tt][h]; } for (int t = 0; t < T; ++t) { f[t][h] = work[t] + work[t + T]; } } for (int t = 0; t < T; ++t) { FFT.invFft(f[t], len); } vector<Mint> cs(TEN[T]); for (int h = 0; h < TEN[T]; ++h) { cs[h] = f[zw[h]][h]; } // cerr<<" return ";pv(cs.begin(),cs.end()); return cs; } vector<Mint> power(vector<Mint> as, Int e) { assert((int)as.size() == TEN[T]); if (T == 0) { return {as[0].pow(e)}; } Mint later = 1; if (e >= 10 * T) { if (!as[0]) { return vector<Mint>(TEN[T], 0); } later = as[0].pow(e); const Mint c = as[0].inv(); for (int h = 0; h < TEN[T]; ++h) { as[h] *= c; } e = 10 * T + (e - 10 * T) % MO; } vector<Mint> bs(TEN[T], 0); bs[0] = 1; for (; e; e >>= 1) { if (e & 1) bs = ei(bs, as); as = ei(as, as); } for (int h = 0; h < TEN[T]; ++h) { bs[h] *= later; } return bs; } int main() { // 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]); } len = 1; for (; len < 2 * TEN[T]; len <<= 1) {} fill(zw, zw + len, 0); 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<<"len = "<<len<<endl; // 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 = power(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; #else break; #endif } return 0; }