結果

問題 No.802 だいたい等差数列
ユーザー ecotteaecottea
提出日時 2023-01-26 16:33:32
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
MLE  
実行時間 -
コード長 8,205 bytes
コンパイル時間 3,705 ms
コンパイル使用メモリ 232,856 KB
実行使用メモリ 816,512 KB
最終ジャッジ日時 2024-06-27 09:55:31
合計ジャッジ時間 6,525 ms
ジャッジサーバーID
(参考情報)
judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample -- * 4
other AC * 24 MLE * 1 -- * 5
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; // -2^63 2^63 = 9 * 10^18int -2^31 2^31 = 2 * 10^9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
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 vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
const vi DX = { 1, 0, -1, 0 }; // 4
const vi DY = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004004004004004LL;
double EPS = 1e-12;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // mod
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
//
template <class T> inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
// Visual Studio
#ifdef _MSC_VER
#include "local.hpp"
// gcc
#else
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define gcd __gcd
#define dump(...)
#define dumpel(v)
#define dump_list(v)
#define dump_list2D(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) while (1) cout << "OLE"; }
#endif
#endif //
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
using mint = modint1000000007;
//using mint = modint998244353;
//using mint = modint; // mint::set_mod(m);
istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>;
#endif
//
/*
* Factorial_mint(int n_max) : O(n_max)
* n_max!
*
* mint factorial(int n) : O(1)
* n!
*
* mint factorial_inv(int n) : O(1)
* 1 / n!
*
* mint inv(int n) : O(1)
* 1 / n
*
* mint permutation(int n, int r) : O(1)
* nPr
*
* mint binomial(int n, int r) : O(1)
* nCr
*
* mint multinomial(vi rs) : O(|rs|)
* nC[rs] n = Σrs
*/
class Factorial_mint {
//
int n_max;
vm fac, fac_inv;
public:
// n! O(n)
Factorial_mint(int n) : n_max(n), fac(n + 1), fac_inv(n + 1) {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
fac[0] = 1;
repi(i, 1, n) fac[i] = fac[i - 1] * i;
fac_inv[n] = fac[n].inv();
repir(i, n - 1, 0) fac_inv[i] = fac_inv[i + 1] * (i + 1);
}
Factorial_mint() : n_max(0) {} //
// n! O(1)
mint factorial(int n) const {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
Assert(0 <= n && n <= n_max);
return fac[n];
}
// 1 / n! O(1)
mint factorial_inv(int n) const {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
Assert(0 <= n && n <= n_max);
return fac_inv[n];
}
// 1 / n O(1)
mint inv(int n) const {
// verify : https://atcoder.jp/contests/exawizards2019/tasks/exawizards2019_d
Assert(0 < n && n <= n_max);
return fac[n - 1] * fac_inv[n];
}
// nPr O(1)
mint permutation(int n, int r) const {
Assert(n <= n_max);
if (r < 0 || n - r < 0) return 0;
return fac[n] * fac_inv[n - r];
}
// nCr O(1)
mint binomial(int n, int r) const {
// verify : https://atcoder.jp/contests/abc034/tasks/abc034_c
Assert(n <= n_max);
if (r < 0 || n - r < 0) return 0;
return fac[n] * fac_inv[r] * fac_inv[n - r];
}
// nC[r] O(|r|)
mint multinomial(const vi& rs) const {
// verify : https://yukicoder.me/problems/no/2141
if (*min_element(all(rs)) < 0) return 0;
int n = accumulate(all(rs), 0);
Assert(n <= n_max);
mint res = fac[n];
repe(r, rs) res *= fac_inv[r];
return res;
}
};
//r n O(n - r)
/*
* i∈[r..n] binomial(i, r)
*/
vm binomial_fixed_r(int n, int r) {
// verify : https://yukicoder.me/problems/no/1102
// fac[i] : i!
vm fac(n - r + 1);
fac[0] = 1;
repi(i, 1, n - r) fac[i] = fac[i - 1] * i;
// fac_inv : 1 / (n - r)!
mint fac_inv = fac[n - r].inv();
// inv[i] : 1 / i
vm inv(n - r + 1);
repir(i, n - r, 1) {
inv[i] = fac[i - 1] * fac_inv;
fac_inv *= i;
}
// bin[i] : bin(r + i, r)
vm bin(n - r + 1);
bin[0] = 1;
repi(i, r + 1, n) bin[i - r] = bin[i - 1 - r] * i * inv[i - r];
return bin;
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
int n, m, d1, d2;
cin >> n >> m >> d1 >> d2;
int k = m - d1 * (n - 1) - 1;
if (k < 0) EXIT(0);
int d = d2 - d1 + 1;
Factorial_mint fm(n + 10);
vm num(k + 1), dnm(k + 1);
rep(i, k + 1) {
if (d * i > k) break;
num[d * i] = (i & 1 ? -1 : 1) * fm.binomial(n - 1, i);
}
auto bin = binomial_fixed_r(n + k, n);
rep(i, k + 1) {
dnm[i] = bin[i];
}
mint res = 0;
rep(i, k + 1) res += num[i] * dnm[k - i];
cout << res << endl;
}
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