Submission #1017321

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Source Code Expand

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

const int M = 100005;
const ll p = 1e9+7;

ll n, a, b, c;
ll fact[M], invfact[M];
ll tot = 0;

ll exp(ll x, ll k) {
	if (k == 0)
		return 1;
	ll y = exp(x, k/2);
	if (k%2 == 0)
		return y*y%p;
	else
		return y*y%p*x%p;
}

ll inv(ll x) { return exp(x, p-2); }

ll binom(ll x, ll y) {
	if (y == 0)
		return 1;
	if (x < y || x < 0 || y < 0)
		return 0;
	return fact[x]*invfact[y]%p*invfact[x-y]%p;
}

int main() {
	cin >> n >> a >> b >> c;
	if (b%2 == 1) {
		cout << "0\n"; return 0;
	}

	fact[0] = invfact[0] = 1;
	for (int i = 1; i < M; ++i) {
		fact[i] = i*fact[i-1]%p;
		invfact[i] = inv(fact[i]);
	}

	for (int i = a+b/2; i <= n; ++i) {
		ll ct = binom(i, b/2)*binom(i-b/2, a)%p;
		ll d = c-3*(i-b/2-a);
		if (d < 0)
			continue;
		ll sum = 0;
		for (int j = 0; j <= d; ++j)
			sum = (sum + binom(b/2+j-1, j)*binom(a, d-j))%p;
		tot = (tot + sum*ct)%p;
	}

	cout << tot << endl;
}

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Judge Result