提出 #61233579

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ソースコード 拡げる

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define fi first
#define se second
const ll mod=1e9+7;
const int N=2e7+5;
const int iu=2e7+3;
ll f[N],inf[N];
ll pw(ll x,ll y){
	if(y==0) return 1;
	if(y%2) return x*pw(x,y-1)%mod;
	ll res=pw(x,y/2);
	return res*res%mod;
}
ll C(int x,int y){
	if(y>x|| y<0) return 0;
	return f[x]*inf[y]%mod*inf[x-y]%mod;
}
ll n,a,b;
int main(){
	ios::sync_with_stdio(false);cin.tie(0);
	f[0]=1;
	for(int i=1; i<=iu ;i++) f[i]=f[i-1]*i%mod;
	inf[iu]=pw(f[iu],mod-2);
	for(int i=iu; i>=1 ;i--) inf[i-1]=inf[i]*i%mod;
	cin >> n >> a >> b;
	ll d=n-a-b;
	ll ans=0;
	for(int i=1; i<=b ;i++){//cycle has i continuous A-blocks and i B-blocks
		ll all=0,end_a=0;
		{
			ll w1=0,w2=0,w3=0;
			w1=C(a-1,i-1)*C(b-1,i-1)%mod;
			w2=C(a-1,i-1)*C(b-1,i)%mod;
			w3=C(a-1,i)*C(b-1,i-1)%mod;
			ll dv=f[a+b-1]*inf[a+b]%mod;
			end_a=(w1+w2+w3+w1)%mod*(a-b)%mod*dv%mod;//out of many cycles this amount catalan
		}
		{
			ll w1=0,w2=0,w3=0;
			w1=C(a,i-1)*C(b-1,i-1)%mod;
			w2=C(a,i-1)*C(b-1,i)%mod;
			w3=C(a,i)*C(b-1,i-1)%mod;
			ll dv=f[a+b]*inf[a+b+1]%mod;
			all=(w1+w2+w3+w1)%mod*(a-b+1)%mod*dv%mod;//out of many cycles this amount catalan
			//cout << i << ' ' << w1 << ' ' << w2 << ' ' << w3 << endl;
		}
		
		all=(all+mod-end_a)%mod;
		//cout << i << ' ' << end_a << ' ' << all << endl;
		ll nd=d-(a+b)+2*i;
		if(nd>=0){
			ans=(ans+all*C(nd+a+b,a+b))%mod;
		}
		++nd;
		if(nd>=0){
			ans=(ans+end_a*C(nd+a+b,a+b))%mod;
		}
	}
	cout << ans << '\n';
}

提出情報

ジャッジ結果