結果

問題 No.802 だいたい等差数列
ユーザー fumofumofunifumofumofuni
提出日時 2022-08-20 15:44:03
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 6,672 bytes
コンパイル時間 2,641 ms
コンパイル使用メモリ 213,408 KB
最終ジャッジ日時 2025-01-31 02:05:14
ジャッジサーバーID
(参考情報)
judge1 / judge5
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 4
other AC * 21 TLE * 9
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

#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(ll i=0;i<n;i++)
#define repl(i,l,r) for(ll i=(l);i<(r);i++)
#define per(i,n) for(ll i=(n)-1;i>=0;i--)
#define perl(i,r,l) for(ll i=r-1;i>=l;i--)
#define fi first
#define se second
#define ins insert
#define pqueue(x) priority_queue<x,vector<x>,greater<x>>
#define all(x) (x).begin(),(x).end()
#define CST(x) cout<<fixed<<setprecision(x)
#define rev(x) reverse(x);
using ll=long long;
using vl=vector<ll>;
using vvl=vector<vector<ll>>;
using pl=pair<ll,ll>;
using vpl=vector<pl>;
using vvpl=vector<vpl>;
const ll MOD=1000000007;
const ll MOD9=998244353;
const int inf=1e9+10;
const ll INF=4e18;
const ll dy[9]={1,0,-1,0,1,1,-1,-1,0};
const ll dx[9]={0,1,0,-1,1,-1,1,-1,0};
template <typename T> inline bool chmax(T &a, T b) {
return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
return ((a > b) ? (a = b, true) : (false));
}
const int mod = MOD;
const int max_n = 2000050;
struct mint {
ll x; // typedef long long ll;
mint(ll x=0):x((x%mod+mod)%mod){}
mint operator-() const { return mint(-x);}
mint& operator+=(const mint a) {
if ((x += a.x) >= mod) x -= mod;
return *this;
}
mint& operator-=(const mint a) {
if ((x += mod-a.x) >= mod) x -= mod;
return *this;
}
mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;}
mint operator+(const mint a) const { return mint(*this) += a;}
mint operator-(const mint a) const { return mint(*this) -= a;}
mint operator*(const mint a) const { return mint(*this) *= a;}
mint pow(ll t) const {
if (!t) return 1;
mint a = pow(t>>1);
a *= a;
if (t&1) a *= *this;
return a;
}
bool operator==(const mint &p) const { return x == p.x; }
bool operator!=(const mint &p) const { return x != p.x; }
// for prime mod
mint inv() const { return pow(mod-2);}
mint& operator/=(const mint a) { return *this *= a.inv();}
mint operator/(const mint a) const { return mint(*this) /= a;}
};
istream& operator>>(istream& is, mint& a) { return is >> a.x;}
ostream& operator<<(ostream& os, const mint& a) { return os << a.x;}
using vm=vector<mint>;
using vvm=vector<vm>;
struct combination {
vector<mint> fact, ifact;
combination(int n):fact(n+1),ifact(n+1) {
assert(n < mod);
fact[0] = 1;
for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i;
ifact[n] = fact[n].inv();
for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i;
}
mint operator()(int n, int k) {
if (k < 0 || k > n) return 0;
return fact[n]*ifact[k]*ifact[n-k];
}
}comb(max_n);
namespace NTT {
// int32modFFTauto c=NTT::mul(a,b,mod)TIME
// ChineseRemlong long
std::vector<int> tmp;
size_t sz = 1;
inline int powMod(int n, int p, int m) {
int res = 1;
while (p) {
if (p & 1) res = (ll)res * n % m;
n = (ll)n * n % m;
p >>= 1;
}
return (int)res;
}
inline int invMod(int n, int m) {
return powMod(n, m - 2, m);
}
template <int Mod, int PrimitiveRoot>
struct NTTPart {
static std::vector<int> ntt(std::vector<int> a, bool inv = false) {
size_t mask = sz - 1;
size_t p = 0;
for (size_t i = sz >> 1; i >= 1; i >>= 1) {
auto& cur = (p & 1) ? tmp : a;
auto& nex = (p & 1) ? a : tmp;
int e = powMod(PrimitiveRoot, (Mod - 1) / sz * i, Mod);
if (inv) e = invMod(e, Mod);
int w = 1;
for (size_t j = 0; j < sz; j += i) {
for (size_t k = 0; k < i; ++k) {
nex[j + k] = (cur[((j << 1) & mask) + k] + (ll)w * cur[(((j << 1) + i) & mask) + k]) % Mod;
}
w = (ll)w * e % Mod;
}
++p;
}
if (p & 1) std::swap(a, tmp);
if (inv) {
int invSz = invMod(sz, Mod);
for (size_t i = 0; i < sz; ++i) a[i] = (ll)a[i] * invSz % Mod;
}
return a;
}
static std::vector<int> mul(std::vector<int> a, std::vector<int> b) {
a = ntt(a);
b = ntt(b);
for (size_t i = 0; i < sz; ++i) a[i] = (ll)a[i] * b[i] % Mod;
a = ntt(a, true);
return a;
}
};
constexpr int M[] = {1224736769, 469762049, 167772161};
constexpr int PR[] = {3, 3, 3};
constexpr int NTT_CONVOLUTION_TIME = 3;
/*
X := max(a)*max(b)*max(|a|, |b|) ,
NTT_CONVOLUTION_TIME <- 1: X < 1224736769 = 1.2*10^ 9 ~ 2^30
NTT_CONVOLUTION_TIME <- 2: X < 575334854091079681 = 5.8*10^17 ~ 2^59
NTT_CONVOLUTION_TIME <- 3: X < 2^86 (32bit * 32bit * 10^7)
*/
inline void garner(std::vector<int> *c, int mod) {
if (NTT_CONVOLUTION_TIME == 1) {
for(auto& x : c[0]) x %= mod;
}
else if (NTT_CONVOLUTION_TIME == 2) {
const int r01 = invMod(M[0], M[1]);
for (size_t i = 0; i < sz; ++i) {
c[1][i] = (c[1][i] - c[0][i]) * (ll)r01 % M[1];
if (c[1][i] < 0) c[1][i] += M[1];
c[0][i] = (c[0][i] + (ll)c[1][i] * M[0]) % mod;
}
}
else if (NTT_CONVOLUTION_TIME == 3) {
const int R01 = invMod(M[0], M[1]);
const int R02 = invMod(M[0], M[2]);
const int R12 = invMod(M[1], M[2]);
const int M01 = (ll)M[0] * M[1] % mod;
for (size_t i = 0; i < sz; ++i) {
c[1][i] = (c[1][i] - c[0][i]) * (ll)R01 % M[1];
if (c[1][i] < 0) c[1][i] += M[1];
c[2][i] = ((c[2][i] - c[0][i]) * (ll)R02 % M[2] - c[1][i]) * R12 % M[2];
if (c[2][i] < 0) c[2][i] += M[2];
c[0][i] = (c[0][i] + (ll)c[1][i] * M[0] + (ll)c[2][i] * M01) % mod;
}
}
}
std::vector<int> mul(std::vector<int> a, std::vector<int> b, int mod) {
for (auto& x : a) x %= mod;
for (auto& x : b) x %= mod;
size_t m = a.size() + b.size() - 1;
sz = 1;
while (m > sz) sz <<= 1;
tmp.resize(sz);
a.resize(sz, 0);
b.resize(sz, 0);
std::vector<int> c[NTT_CONVOLUTION_TIME];
if (NTT_CONVOLUTION_TIME >= 1) c[0] = NTTPart<M[0], PR[0]>::mul(a, b);
if (NTT_CONVOLUTION_TIME >= 2) c[1] = NTTPart<M[1], PR[1]>::mul(a, b);
if (NTT_CONVOLUTION_TIME >= 3) c[2] = NTTPart<M[2], PR[2]>::mul(a, b);
for (auto& v : c) v.resize(m);
garner(c, mod);
return c[0];
}
}; // !!! CHECK NTT_CONVOLUTION_TIME !!!
int main(){
ll n,m;cin >> n >> m;
ll x,y;cin >> x >> y;
m-=x*(n-1);y-=x;
if(m<=0){
cout << 0 << endl;return 0;
}
vector<int> dp(m);
ll cnt=0;
for(ll i=0;i<m;i+=y+1){
if(cnt&1)dp[i]=(int)((comb(n-1,cnt)*-1).x);
else dp[i]=(int)((comb(n-1,cnt)).x);
cnt++;
}
vector<int> ndp(m);
for(ll i=0;i<m;i++){
ndp[i]=(int)comb(n-2+i,n-2).x;
}
vector<int> sdp(m,1);
//rep(i,m)cout << dp[i] <<" ";cout << endl;
//rep(i,m)cout << ndp[i] <<" ";cout << endl;
//rep(i,m)cout << sdp[i] <<" ";cout << endl;
auto f=NTT::mul(dp,ndp,MOD);
f=NTT::mul(f,sdp,MOD);
mint ans=0;
for(ll i=0;i<m;i++)ans+=f[i];
cout << ans << endl;
}
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