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>
using namespace std;
const int N=2005;
const int M=N*N;
const int mo=1e9+7;
int n,k,m;
long long p[M],q[M],f[N][N];
long long ksm(long long x,int y)
{
	long long t=1;
	for (;y;y>>=1)
	{
		if (y&1) t=t*x%mo;
		x=x*x%mo;
	}
	return t;
}
long long c(int x,int y){return p[x]*q[y]%mo*q[x-y]%mo;}
int main()
{
	scanf("%d%d",&n,&k),m=n*k;
	if (k==1){printf("1");return 0;}
	p[0]=q[0]=1;
	for (int i=1;i<=m;i++) p[i]=p[i-1]*i%mo;
	q[m]=ksm(p[m],mo-2);
	for (int i=m-1;i;i--) q[i]=q[i+1]*(i+1)%mo;
	f[0][0]=1;
	for (int i=1;i<=n;i++)
		for (int j=i;j>=0;j--)
		{
			f[i][j]=f[i][j+1];
			if (j) f[i][j]=(f[i][j]+f[i-1][j-1]*c(i*k-j-1,k-2))%mo;
		}
	printf("%lld",f[n][0]*p[n]%mo);
	return 0;
}