Submission #1001053

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Source Code Expand

#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define all(c) c.begin(),c.end()
#define pb push_back
#define fs first
#define sc second
#define show(x) cout << #x << " = " << x << endl
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)
using namespace std;
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){return o<<"("<<p.fs<<","<<p.sc<<")";}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){o<<"sz = "<<vc.size()<<endl<<"[";for(const T& v:vc) o<<v<<",";o<<"]";return o;}
typedef long long ll;
ll mod=1e9+7;
const int MX=50000;
ll f[MX+1],g[MX+1],inv[MX+1];
void precalc(){
	f[0]=1;
	rep1(i,MX) f[i]=f[i-1]*i%mod;
	inv[1]=1;
	for(int i=2;i<=MX;i++) inv[i]=mod-mod/i*inv[mod%i]%mod;
	g[0]=1;
	rep1(i,MX) g[i]=g[i-1]*inv[i]%mod;
}
ll C4(int a,int b,int c,int d){
	return f[a+b+c+d]*g[a]%mod*g[b]%mod*g[c]%mod*g[d]%mod;
}
ll C2(int a,int b){
	if(b==0) return 1;
	if(a<b) return 0;
	return f[a]*g[b]%mod*g[a-b]%mod;
}
int main(){
	precalc();
	int N,A,B,C;
	cin>>N>>A>>B>>C;
	if(B%2==1){
		puts("0");
		return 0;
	}
	ll ans=0;
	rep(i,A+1){
		rep(j,C/3+1){
			int l=C-(A-i)-3*j;
			if(l<0) break;
			ll tmp=C4(i,A-i,j,B/2);
			tmp*=C2(l+B/2-1,l);
			tmp%=mod;
			ans+=tmp;
			ans%=mod;
		}
	}
	cout<<ans<<endl;
}

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