結果
| 問題 | No.3415 Dial Lock |
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2025-12-22 00:33:19 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 3,484 ms / 10,000 ms |
| コード長 | 12,563 bytes |
| 記録 | |
| コンパイル時間 | 1,696 ms |
| コンパイル使用メモリ | 132,796 KB |
| 実行使用メモリ | 24,620 KB |
| 最終ジャッジ日時 | 2025-12-22 00:34:21 |
| 合計ジャッジ時間 | 53,214 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 18 |
コンパイルメッセージ
main.cpp: In function ‘int main()’:
main.cpp:327:38: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
327 | for (int n = 0; n < N; ++n) scanf("%d", &A[n]);
| ~~~~~^~~~~~~~~~~~~
main.cpp:329:66: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
329 | for (int k = 0; k < K; ++k) for (int n = 0; n < N; ++n) scanf("%d", &R[k][n]);
| ~~~~~^~~~~~~~~~~~~~~~
ソースコード
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <chrono>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#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> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
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; }
#define COLOR(s) ("\x1b[" s "m")
////////////////////////////////////////////////////////////////////////////////
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;
}
// cs[k] = \sum[i-j=k] as[i] bs[j] (0 <= k <= m-n)
vector<ModInt<M>> middle(vector<ModInt<M>> as, vector<ModInt<M>> bs) const {
const int m = as.size(), n = bs.size();
assert(m >= n); assert(n >= 1);
int len = 1;
for (; len < m; len <<= 1) {}
as.resize(len, 0);
fft(as);
std::reverse(bs.begin(), bs.end());
bs.resize(len, 0);
fft(bs);
for (int i = 0; i < len; ++i) as[i] *= bs[i];
invFft(as);
as.resize(m);
as.erase(as.begin(), as.begin() + (n - 1));
return as;
}
};
constexpr int MO = 120586241;
using Mint = ModInt<MO>;
const Fft<MO, 6, 20> FFT;
const Mint W = Mint(6).pow((MO - 1) / 10);
Mint WW[11];
int TEN[6];
int N, K;
Int T;
vector<int> A;
vector<vector<int>> R;
void dft(vector<Mint> &fs) {
for (int n = 0; n < N; ++n) {
for (int u0 = 0; u0 < TEN[N]; u0 += TEN[n + 1]) {
for (int u = u0; u < u0 + TEN[n]; ++u) {
Mint as[10] = {}, bs[10] = {};
for (int i = 0; i < 10; ++i) as[i] = fs[u + i * TEN[n]];
for (int i = 0; i < 10; ++i) for (int j = 0; j < 10; ++j) bs[j] += WW[(i * j) % 10] * as[i];
for (int i = 0; i < 10; ++i) fs[u + i * TEN[n]] = bs[i];
}
}
}
}
using Poly = vector<Mint>;
Poly operator+(const Poly &as, const Poly &bs) {
Poly cs(max(as.size(), bs.size()), 0);
for (int i = 0; i < (int)as.size(); ++i) cs[i] += as[i];
for (int i = 0; i < (int)bs.size(); ++i) cs[i] += bs[i];
return cs;
}
Poly operator*(const Poly &as, const Poly &bs) {
return FFT.convolve(as, bs);
}
pair<Poly, Poly> solve(const vector<Mint> &base, const vector<int> &tar) {
// f[n] = \sum[u] coef[u] base[u]^n
const Mint invTen = Mint(TEN[N]).inv();
queue<pair<Poly, Poly>> que;
for (int u = 0; u < TEN[N]; ++u) {
Mint coef = invTen;
for (int n = 0; n < N; ++n) {
const int i = u / TEN[n] % 10;
const int j = tar[n];
coef *= WW[10 - (i * j) % 10];
}
que.emplace(Poly{coef}, Poly{1, -base[u]});
}
for (; que.size() >= 2; ) {
const auto a = que.front(); que.pop();
const auto b = que.front(); que.pop();
que.emplace(a.first * b.second + a.second * b.first, a.second * b.second);
}
return que.front();
}
Mint divAt(vector<Mint> ps, vector<Mint> qs, Int n) {
for (; n; n >>= 1) {
Poly neg = qs;
for (int i = 1; i < (int)neg.size(); i += 2) neg[i] = -neg[i];
Poly pps = ps * neg;
Poly qqs = qs * neg;
ps.clear();
qs.clear();
for (int i = n & 1; i < (int)pps.size(); i += 2) ps.push_back(pps[i]);
for (int i = 0 ; i < (int)qqs.size(); i += 2) qs.push_back(qqs[i]);
}
return ps[0] / qs[0];
}
int main() {
for (int i = 0; i <= 10; ++i) WW[i] = W.pow(i);
TEN[0] = 1;
for (int i = 1; i <= 5; ++i) TEN[i] = TEN[i - 1] * 10;
for (; ~scanf("%d%d%lld", &N, &K, &T); ) {
A.resize(N);
for (int n = 0; n < N; ++n) scanf("%d", &A[n]);
R.assign(K, vector<int>(N));
for (int k = 0; k < K; ++k) for (int n = 0; n < N; ++n) scanf("%d", &R[k][n]);
const Mint invK = Mint(K).inv();
vector<Mint> fs(TEN[N], 0);
for (int k = 0; k < K; ++k) {
int u = 0;
for (int n = 0; n < N; ++n) u += R[k][n] * TEN[n];
fs[u] += invK;
}
dft(fs);
const auto p = solve(fs, A);
const auto q = solve(fs, vector<int>(N, 0));
// [x^T] (1/(1-x)) (p/q)
const Poly numer = p.first * q.second;
const Poly denom = p.second * q.first * Poly{1, -1};
const Mint ans = divAt(numer, denom, T);
printf("%u\n", ans.x);
}
return 0;
}