結果
| 問題 |
No.1783 Remix Sum
|
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2021-12-12 00:59:17 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 12,995 bytes |
| コンパイル時間 | 2,509 ms |
| コンパイル使用メモリ | 140,240 KB |
| 実行使用メモリ | 16,620 KB |
| 最終ジャッジ日時 | 2024-07-20 08:57:45 |
| 合計ジャッジ時間 | 68,428 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 75 WA * 1 |
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) {
if (T == 0) {
return {as[0] * bs[0]};
}
// 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) {
if (e >= 10 && !as[0]) {
return vector<Mint>(TEN[T], 0);
}
Mint later = 1;
if (as[0]) {
later = as[0].pow(e);
const Mint c = as[0].inv();
for (int h = 0; h < TEN[T]; ++h) {
as[h] *= c;
}
}
if (e >= 10) {
e = 10 + (e - 10) % 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;
#endif
}
return 0;
}