結果
| 問題 |
No.1783 Remix Sum
|
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2021-12-12 04:50:41 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 16,333 bytes |
| コンパイル時間 | 5,673 ms |
| コンパイル使用メモリ | 258,892 KB |
| 実行使用メモリ | 24,640 KB |
| 最終ジャッジ日時 | 2024-07-20 13:56:18 |
| 合計ジャッジ時間 | 45,997 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 74 TLE * 2 |
ソースコード
// #pragma GCC optimize("O3,unroll-loops")
#pragma GCC optimize("Ofast")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif
template <typename T> T rd_integer() {
T ret = 0;
bool minus = false;
char c = getchar_unlocked();
while (!isdigit(c)) minus |= (c == '-'), c = getchar_unlocked();
while (isdigit(c)) ret = (ret << 1) + (ret << 3) + (c ^ 48), c = getchar_unlocked();
return minus ? -ret : ret;
}
int rdi() { return rd_integer<int>(); }
long long rdll() { return rd_integer<long long>(); }
template <typename T> void wt_integer(T x, char delim) {
if (x == 0) {
putchar('0'), putchar(delim);
return;
}
if (x < 0) putchar('-'), x = -x;
static char cache[20];
char *head = cache;
while (x) *head = '0' + x % 10, head++, x /= 10;
while (head != cache) putchar(*(--head));
putchar(delim);
}
constexpr int md = (115 << 20) + 1;
#include <atcoder/modint>
using mint = atcoder::static_modint<md>;
#include <atcoder/convolution>
// Multivariate convolution (Linear, overflow cutoff)
// Complexity: (kN \log N + k^2 N)$
// Note that the vectors store the infomation in **column-major order**
// Implementation idea: https://rushcheyo.blog.uoj.ac/blog/6547
// Details of my implementation: https://hitonanode.github.io/cplib-cpp/convolution/multivar_ntt.hpp
template <typename MODINT> struct multivar_ntt {
int K, N, fftlen;
std::vector<int> dim;
std::vector<char> chi;
MODINT invfftlen;
vector<MODINT> g;
std::vector<std::vector<MODINT>> gex, hex;
vector<vector<int>> chi2i;
private:
void _initialize(const std::vector<int> &dim_) {
dim = dim_;
K = dim_.size();
N = std::accumulate(dim_.begin(), dim_.end(), 1, [&](int l, int r) { return l * r; });
fftlen = 1;
while (fftlen < N * 2) fftlen <<= 1;
invfftlen = MODINT(fftlen).inv();
chi.resize(fftlen);
int t = 1;
for (auto d : dim_) {
t *= d;
for (int s = t; s < fftlen; s += t) chi[s] += 1;
}
for (int i = 0; i + 1 < fftlen; i++) {
chi[i + 1] += chi[i];
if (chi[i + 1] >= K) chi[i + 1] -= K;
}
chi2i.assign(K, {});
if (K) {
for (int i = 0; i < N; ++i) chi2i[chi[i]].push_back(i);
}
}
public:
void operator()(std::vector<MODINT> &f) {
assert(int(f.size()) == N);
assert(int(g.size()) == N);
if (dim.empty()) {
f[0] *= g[0];
return;
}
hex.assign(K, std::vector<MODINT>(fftlen));
vector<MODINT> fexdf(fftlen);
for (int df = 0; df < K; ++df) {
fexdf.assign(fftlen, 0);
for (auto i : chi2i[df]) {
fexdf[i] = f[i];
}
atcoder::internal::butterfly(fexdf);
for (int dg = 0; dg < K; dg++) {
int dh = (df + dg < K) ? df + dg : df + dg - K;
for (int i = 0; i < fftlen; i++) hex[dh][i] += fexdf[i] * gex[dg][i];
}
}
for (auto &vec : hex) atcoder::internal::butterfly_inv(vec);
for (int i = 0; i < N; i++) f[i] = hex[chi[i]][i] * invfftlen;
}
multivar_ntt(const std::vector<int> &dim_) { _initialize(dim_); }
void set_g(const vector<MODINT> &g_) {
g = g_;
gex.assign(K, vector<MODINT>(fftlen));
if (dim.empty()) return;
for (int i = 0; i < N; i++) gex[chi[i]][i] = g[i];
for (auto &vec : gex) atcoder::internal::butterfly(vec);
}
void double_g() {
if (!K) {
g[0] *= g[0];
return;
}
vector<MODINT> ftmp(K), gtmp(K * 2);
for (int i = 0; i < fftlen; ++i) {
gtmp.assign(K * 2, 0);
for (int k = 0; k < K; ++k) ftmp[k] = gex[k][i], gtmp[k * 2] = ftmp[k] * ftmp[k];
for (int k = 0; k < K; ++k) {
for (int l = 0; l < k; ++l) gtmp[k + l] += ftmp[k] * ftmp[l] * 2;
}
for (int k = 0; k < K; ++k) gex[k][i] = gtmp[k] + gtmp[k + K];
}
for (auto &vec : gex) atcoder::internal::butterfly_inv(vec);
for (int i = 0; i < N; ++i) g[i] = gex[chi[i]][i] * invfftlen;
gex.assign(K, vector<MODINT>(fftlen));
for (int i = 0; i < N; i++) gex[chi[i]][i] = g[i];
for (auto &vec : gex) atcoder::internal::butterfly(vec);
}
};
void ntt(vector<mint> &vec, bool tf) {
if (tf) {
atcoder::internal::butterfly_inv(vec);
mint szinv = mint(vec.size()).inv();
for (auto &x : vec) x *= szinv;
} else {
atcoder::internal::butterfly(vec);
}
}
template <typename ModInt> std::vector<ModInt> inv_of_poly_mod_monomial(const std::vector<ModInt> &f, int l) {
assert(l > 0);
if (f.empty()) return {};
const ModInt ret0 = f[0].inv();
if (ret0 * f[0] != ModInt(1)) return {};
std::vector<ModInt> ret{ret0};
unsigned sz = 1;
while (ret.size() < l) {
std::vector<ModInt> h0(sz * 2), h1(sz * 2), a(sz * 2);
std::copy(ret.begin(), ret.end(), a.begin());
std::copy(f.begin(), f.begin() + std::min<unsigned>(sz, f.size()), h0.begin());
if (int(f.size()) >= sz) std::copy(f.begin() + sz, f.begin() + std::min<unsigned>(sz * 2, f.size()), h1.begin());
ntt(a, false);
ntt(h0, false);
ntt(h1, false);
for (unsigned i = 0; i < sz * 2; i++) h0[i] *= a[i];
for (unsigned i = 0; i < sz * 2; i++) h1[i] *= a[i];
ntt(h0, true);
ntt(h1, true);
for (unsigned i = 0; i < sz; i++) h1[i] += h0[i + sz];
std::fill(h1.begin() + sz, h1.end(), 0);
ntt(h1, false);
for (unsigned i = 0; i < sz * 2; i++) h1[i] *= a[i];
ntt(h1, true);
ret.resize(std::min<unsigned>(sz * 2, l));
for (unsigned i = sz; i < ret.size(); i++) ret[i] = -h1[i - sz];
sz *= 2;
}
return ret;
}
// https://uoj.ac/submission/460059
using fps = vector<mint>;
fps multi_inv(const fps &f, const vector<int> &base) {
assert(!f.empty() && f[0] != 0);
int n = f.size(), s = base.size(), W = 1;
while (W < 2 * n) W *= 2;
vector<int> chi(W);
for (int i = 0; i < W; i++) {
int x = i;
for (int j = 0; j < s - 1; j++) chi[i] += (x /= base[j]);
chi[i] %= s;
}
auto hadamard_prod = [&s](vector<fps> &F, vector<fps> &G, vector<fps> &H) {
fps a(s);
for (int k = 0; k < (int)F[0].size(); k++) {
fill(begin(a), end(a), typename fps::value_type());
for (int i = 0; i < s; i++)
for (int j = 0; j < s; j++) { a[i + j - (i + j >= s ? s : 0)] += F[i][k] * G[j][k]; }
for (int i = 0; i < s; i++) H[i][k] = a[i];
}
};
fps g(W);
g[0] = f[0].inv();
for (int d = 1; d < n; d *= 2) {
vector<fps> F(s, fps(2 * d)), G(s, fps(2 * d)), H(s, fps(2 * d));
for (int j = 0; j < min((int)f.size(), 2 * d); j++) F[chi[j]][j] = f[j];
for (int j = 0; j < d; j++) G[chi[j]][j] = g[j];
for (auto &x : F) ntt(x, false);
for (auto &x : G) ntt(x, false);
hadamard_prod(F, G, H);
for (auto &x : H) ntt(x, true);
for (auto &x : F) fill(begin(x), end(x), typename fps::value_type());
for (int j = d; j < 2 * d; j++) F[chi[j]][j] = H[chi[j]][j];
for (auto &x : F) ntt(x, false);
hadamard_prod(F, G, H);
for (auto &x : H) ntt(x, true);
for (int j = d; j < 2 * d; j++) g[j] = -H[chi[j]][j];
}
return {begin(g), begin(g) + n};
}
int main() {
auto START = std::chrono::system_clock::now();
constexpr int E = 10;
const mint r10 = 9142366;
int N = rdi(), K = rdi();
lint M = rdll();
int T = rdi();
// M %= mint::mod() - 1;
int K10 = 1;
REP(t, K) K10 *= 10;
vector<int> diminfo(T, E); // T 桁切捨，K - T 桁周期
multivar_ntt<mint> mntt(diminfo);
vector nttmat(E, vector<mint>(E));
REP(i, nttmat.size()) REP(j, nttmat[i].size()) nttmat[i][j] = r10.pow(i * j);
auto inttmat = nttmat;
for (auto &vec : inttmat) for (auto &x : vec) x = x.inv() / mint(10);
auto ntt10 = [&](const array<mint, 10> &v) {
array<mint, 10> ret;
ret.fill(0);
REP(i, E) REP(j, E) ret[i] += nttmat[i][j] * v[j];
return ret;
};
auto intt10 = [&](const array<mint, 10> &v) {
array<mint, 10> ret;
ret.fill(0);
REP(i, E) REP(j, E) ret[i] += inttmat[i][j] * v[j];
return ret;
};
auto circular_ntt = [&](vector<mint> &f) {
for (int di = mntt.N; di < K10; di *= 10) {
for (int l = 0; l < K10; l += di * 10) {
for (int i = l; i < l + di; ++i) {
// [i, i + di, i + 2di, ..., i + 9di] を NTT
auto impose_ntt = [&](vector<mint> &v) {
static array<mint, 10> ntttmp;
ntttmp.fill(0);
REP(k, E) ntttmp[k] = v[i + k * di];
ntttmp = ntt10(ntttmp);
REP(k, E) v[i + k * di] = ntttmp[k];
};
impose_ntt(f);
}
}
}
};
auto circular_intt = [&](vector<mint> &g) {
for (int di = mntt.N; di < K10; di *= 10) {
for (int l = 0; l < K10; l += di * 10) {
for (int i = l; i < l + di; ++i) {
// [i, i + di, i + 2di, ..., i + 9di] を NTT
auto impose_intt = [&](vector<mint> &v) {
static array<mint, 10> ntttmp;
REP(k, E) ntttmp[k] = v[i + k * di];
ntttmp = intt10(ntttmp);
REP(k, E) v[i + k * di] = ntttmp[k];
};
impose_intt(g);
}
}
}
};
vector<mint> dp(K10), trans(K10);
dp[0] = 1;
while (N--) trans[rdi()] += 1;
circular_ntt(dp);
circular_ntt(trans);
// 寝たい
for (int l = 0; l < K10; l += mntt.N) {
vector<mint> fsub(dp.begin() + l, dp.begin() + l + mntt.N);
vector<mint> gsub(trans.begin() + l, trans.begin() + l + mntt.N);
lint p = M;
if (gsub[0] == 0) chmin(p, 100000LL);
else if (T > 0 and __builtin_popcountll(p) > __builtin_popcountll(p + 1) + 15) {
// すみません...
dbg("red");
p++;
auto ginv = multi_inv(gsub, mntt.dim);
mntt.set_g(ginv);
mntt(fsub);
}
// Multivar pow なにもわからない......
mntt.set_g(gsub);
while (p) {
if (p & 1) mntt(fsub);
p /= 2;
if (!p) break;
mntt.double_g();
}
REP(i, fsub.size()) dp[i + l] = fsub[i];
}
circular_intt(dp);
// #ifndef HITONANODE_LOCAL
for (auto x : dp) wt_integer(x.val(), '\n');
// #endif
int64_t spent_ms = std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now() - START).count();
dbg(spent_ms);
}