化分数

划分数
与n个无区别的物品，将它们划分成不超过m组，求出划分方法的个数并对M取模。

1<=m<=n<=1000

input
n = 4
m = 3
output
4 (1+1+2 = 1+3 = 2+2 = 4)

递推式：dp[i][j] = dp[i][j-i] + dp[i-1][j]

#include <stdio.h>
#define M 100000007
int dp[1001][1001];
int main() {
	int n, m;
	scanf("%d%d",&n,&m);
	dp[0][0] = 1;
	for(int i = 1; i <= m; i++) {
		for(int j = 0; j <= n; j++) {
			if(j >= i) {
				dp[i][j] = (dp[i-1][j] + dp[i][j-i]) % M;
			}
			else {
				dp[i][j] = dp[i-1][j];
			}
		}
	}
	printf("%d\n",dp[m][n]);
	return 0;
}