Problem: Snuke loves colorful balls. He has a total of N×K balls, K in each of his favorite N colors. The colors are numbered 1 through N.

He will arrange all of the balls in a row from left to right, in arbitrary order. Then, for each of the N colors, he will paint the leftmost ball of that color into color 0, a color different from any of the N original colors.

After painting, how many sequences of the colors of the balls are possible? Find this number modulo 10^9+7.

Constraints

* 1≤N,K≤2,000

Input

The input is given from Standard Input in the following format:


N K


Output

Print the number of the possible sequences of the colors of the balls after painting, modulo 10^9+7.

Examples

Input

2 2


Output

4


Input

3 1


Output

1


Input

2 3


Output

14


Input

2000 2000


Output

546381702

Solution (in CPP):

Solution:
#include<bits/stdc++.h>

using namespace std;
typedef long long ll;

const int N=2005,M=4000005,P=1E9+7;

int fac[M],ifac[M],n,K,m,dp[N][N];
inline int power(int a,int t){static int r;for(r=1;t;a=(ll)a*a%P,t>>=1)if(t&1)r=(ll)r*a%P;return r;}
inline int C(int n,int m){return(ll)fac[n]*ifac[m]%P*ifac[n-m]%P;}

int main(){
	scanf("%d%d",&n,&K);
	if(K==1)puts("1"),exit(0);
	m=n*K,fac[0]=1;
	for(int i=1;i<=m;i++)fac[i]=(ll)fac[i-1]*i%P;
	ifac[m]=power(fac[m],P-2);
	for(int i=m;i>=1;i--)ifac[i-1]=(ll)ifac[i]*i%P;
	dp[0][0]=1;
	for(int i=1;i<=n;i++)for(int j=0;j<=i;j++){
		if(j)dp[i][j]=dp[i][j-1];
		dp[i][j]=(dp[i][j]+(ll)dp[i-1][j]*C(i*(K-1)+j-1,K-2))%P;
	}
	printf("%d\n",(ll)dp[n][n]*fac[n]%P);
	return 0;
}