Submission #1001647

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Source Code Expand

#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <vector>
#include <map>
#include <set>
#include <string>
#include <cstdlib>
#include <ctime>
#include <deque>
using namespace std;
 
#define P 1000000007
int N, A, B, C;
int co[5010][5010];
int dp[2511][5010][2];
int ans;
 
void up(int &x, int y) {
	x = (x + y) % P;
}
 
int main() {
	cin >> N >> A >> B >> C;
	co[0][0] = 1;
	for (int i = 1; i <= 5000; i++) {
		co[i][0] = 1;
		for (int j = 1; j <= i; j++)
			co[i][j] = (co[i - 1][j] + co[i - 1][j - 1]) % P;
	}
	if (B % 2 != 0) {
		printf("0\n");
		return 0;
	}
	dp[0][0][0] = 1;
	for (int i = 0; i <= N / 2; i++)
		for (int j = 0; j <= N; j++) {
			if (dp[i][j][1]) {
				up(dp[i][j][0], dp[i][j][1]);
				up(dp[i][j + 1][1], dp[i][j][1]);
			}
			if (dp[i][j][0]) {
				up(dp[i + 1][j][1], dp[i][j][0]);
				// up(dp[i + 1][j][0], dp[i][j][0]);
			}
		}
	// for (int i = 0; i <= N / 3; i++)
	for (int j = 0; j <= C; j++)
		if (dp[B / 2][j][0])
			for (int q = 0; j + 3 * q <= C; q++) {
			// if ((B - 2 * i) % 2 != 0)
			// 	continue;
			int aa = C - j - 3 * q, bb = q, cc = A - aa;
			// printf("?? %d %d %d %d %d\n", i, j, aa, bb, cc);
			if (aa < 0 || cc < 0)
				continue;
			// printf("?? %d %d %d %d %d %d\n", i, j, aa, bb, cc, dp[i][j][0]);

			int tmp = dp[B / 2][j][0];
			tmp = 1LL * tmp * co[B / 2 + aa][aa] % P;
			tmp = 1LL * tmp * co[B / 2 + aa + bb][bb] % P;
			tmp = 1LL * tmp * co[B / 2 + aa + bb + cc][cc] % P;
			// tmp = 1LL * tmp * co[i + aa + bb + cc][cc] % P;
			// tmp = 1LL * tmp * co[i + aa + bb + cc + q][q] % P;
			
			up(ans, tmp);
		}
	printf("%d\n", ans);
}

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