結果

問題 No.2120 場合の数の下8桁
ユーザー nagisa5101
提出日時 2023-03-30 02:26:58
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
RE  
実行時間 -
コード長 5,416 bytes
コンパイル時間 4,297 ms
コンパイル使用メモリ 265,608 KB
最終ジャッジ日時 2025-02-11 19:03:36
ジャッジサーバーID
(参考情報)
judge4 / judge4
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ファイルパターン 結果
other AC * 18 WA * 1 RE * 1
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ソースコード

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プレゼンテーションモードにする

#include <bits/stdc++.h>
#include <atcoder/all>
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
using namespace atcoder;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repll(i, n) for (long long i = 0; i < (long long)(n); i++)
#define rep2(i, n, m) for (int i = n; i < (int)(m); i++)
#define repll2(i, n, m) for (long long i = n; i < (long long)(m); i++)
#define all(v) v.begin(),v.end()
using ll=long long;
using ld=long double;
using vi=vector<int>;
using vvi=vector<vi>;
using vvvi=vector<vvi>;
using vl=vector<ll>;
using vvl=vector<vl>;
using vvvl=vector<vvl>;
using vld=vector<ld>;
using vvld=vector<vld>;
int dx[8]={1,0,-1,0,1,1,-1,-1};
int dy[8]={0,1,0,-1,1,-1,1,-1};
const double PI = acos(-1);
//const ll MOD=1e9+7;
//const ll MOD=998244353;
const ll INF=(1LL<<60);
const int INF2=(1<<30);
//using mint=modint1000000007;
//using mint=modint998244353;
// referece: https://37zigen.com/linear-sieve/
class LinearSieve {
public:
LinearSieve(unsigned int n) : _n(n), min_prime_factor(std::vector<unsigned int>(n + 1)) {
std::iota(min_prime_factor.begin(), min_prime_factor.end(), 0);
prime_list.reserve(_n + 1);
for (unsigned int d = 2; d <= _n; ++d) {
if (min_prime_factor[d] == d) {
prime_list.push_back(d);
}
unsigned int prime_max = std::min(min_prime_factor[d], _n / d);
for (unsigned int prime : prime_list) {
if (prime > prime_max) {
break;
}
min_prime_factor[prime * d] = prime;
}
}
}
unsigned int prime_num() const {
return prime_list.size();
}
const std::vector<unsigned int>& get_prime_list() const {
return prime_list;
}
const std::vector<unsigned int>& get_min_prime_factor() const {
return min_prime_factor;
}
private:
const unsigned int _n;
std::vector<unsigned int> min_prime_factor;
std::vector<unsigned int> prime_list;
};
template <typename mint>
class ArbitraryModBinomialCoefficients {
public:
ArbitraryModBinomialCoefficients(unsigned int N) :
_N(N), _M(mint::mod()), _sieve(LinearSieve(N)), _binom(std::vector<mint>(N + 1)) {
solve();
}
mint operator[](unsigned int k) const {
return _binom[k];
}
const std::vector<mint>& get_coeffs() const {
return _binom;
}
const LinearSieve& get_sieve() const {
return _sieve;
}
private:
const unsigned int _N, _M;
const LinearSieve _sieve;
std::vector<mint> _binom;
void mod_invs(std::vector<mint>& invs) {
auto &mpf = _sieve.get_min_prime_factor();
if (_N >= 1) invs[1] = 1;
for (unsigned int i = 2; i <= _N; ++i) {
unsigned int pf = mpf[i];
if (pf == i) {
if (_M % pf) invs[i] = mint(i).inv();
} else {
invs[i] = invs[pf] * invs[i / pf];
}
}
}
void solve() {
auto &primes = _sieve.get_prime_list();
std::vector<unsigned int> d(_N + 1, 0);
std::vector<unsigned int> p;
for (unsigned int prime : primes) {
if (_M % prime) continue;
p.push_back(prime);
unsigned int sz = p.size();
for (unsigned int v = prime; v <= _N; v += prime) {
d[v] = sz;
}
}
const unsigned int L = p.size();
p.insert(p.begin(), 0);
std::vector<mint> invs(_N + 1);
mod_invs(invs);
std::vector<std::vector<mint>> powers(L + 1);
for (unsigned int i = 1; i <= L; ++i) {
unsigned int max_index = _N / (p[i] - 1);
powers[i].resize(max_index + 1);
mint pi = p[i];
powers[i][0] = 1;
for (unsigned int j = 0; j < max_index; ++j) {
powers[i][j + 1] = powers[i][j] * pi;
}
}
const unsigned int half = (_N + 1) / 2;
mint S = 1;
std::vector<unsigned int> T(L + 1, 0);
_binom[0] = 1;
for (unsigned int k = 1; k <= half; ++k) {
unsigned int num = _N - k + 1, den = k;
while (d[num]) ++T[d[num]], num /= p[d[num]];
while (d[den]) --T[d[den]], den /= p[d[den]];
S *= num * invs[den];
_binom[k] = S;
for (unsigned int i = 1; i <= L; ++i) {
_binom[k] *= powers[i][T[i]];
}
}
for (unsigned int k = half + 1; k <= _N; ++k) {
_binom[k] = _binom[_N - k];
}
}
};
int main() {
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
using mint=atcoder::modint;
mint::set_mod(100000000);
int m,n;cin>>m>>n;
ArbitraryModBinomialCoefficients<mint> AMBC(m);
int v=AMBC[n].val();
string ans=to_string(v);
while(int(ans.size())<8)ans='0'+ans;
cout<<ans<<endl;
return 0;
}
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