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>
#define rg register
using namespace std;
const int mod=1e9+7;
#define _ 2001
int n, k, f[_][_], sum[_*_], inv[_*_];
int qp(int x, int y){
	int ans=1;
	while(y){
		if(y&1)ans=1ll*ans*x%mod;
		x=1ll*x*x%mod, y>>=1;
	}return ans;
}
int C(int m, int r){return 1ll*sum[m]*inv[r]%mod*inv[m-r]%mod;}
int main(){
	inv[0]=inv[1]=sum[0]=sum[1]=1;
	for(rg int i=2; i<=2000*2000; ++i)
		sum[i]=1ll*sum[i-1]*i%mod, inv[i]=qp(sum[i], mod-2);
	scanf("%d%d", &n, &k);
	if(k==1){puts("1"); return 0;}
	f[0][0]=1;
	for(int i=1; i<=n; ++i)
		for(int j=0; j<=i; ++j){
			f[i][j]=f[i-1][j];
			if(j)(f[i][j]+=1ll*C((n-j+1)*(k-1)+n-i-1, k-2)*f[i][j-1]%mod)%=mod;
		}
	for(int i=2; i<=n; ++i)
		f[n][n]=1ll*f[n][n]*i%mod;
	printf("%d", f[n][n]);
}