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<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
const int md=1000000007;
int n,K,i,j,f[2005][2005],jc[4000005],rjc[4000005],inv[4000005];
int C(int n,int m)
{
	return 1ll*jc[n]*rjc[m]%md*rjc[n-m]%md;
}
int main()
{
	scanf("%d%d",&n,&K);
	if(K==1)
	{
		printf("1");
		return 0;
	}
	inv[1]=1;
	for(i=2;i<=n*K;++i)
		inv[i]=1ll*inv[md%i]*(md-md/i)%md;
	jc[0]=rjc[0]=1;
	for(i=1;i<=n*K;++i)
	{
		jc[i]=1ll*jc[i-1]*i%md;
		rjc[i]=1ll*rjc[i-1]*inv[i]%md;
	}
	f[1][0]=1;
	for(i=1;i<=n;++i)
		for(j=0;j<=i;++j)
		{
			if(i<n)
				f[i+1][j]=(f[i+1][j]+f[i][j])%md;
			if(j<i)
				f[i][j+1]=(f[i][j+1]+1ll*f[i][j]*(n-j)%md*C(n*K-i-j*(K-1)-1,K-2))%md;
		}
	printf("%d",f[n][n]);
	return 0;
}