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;

const int N=2010,mo=int(1e9+7);
int n,k,f[N][N],fac[N*N],ifac[N*N];

int qpow(int a,int b)
{
	int x=a;  a=1;
	while (b)
		{
			if (b&1)  a=1LL*a*x%mo;
			x=1LL*x*x%mo,b>>=1;
		}
	return a;
}

int C(int n,int m){return 1LL*fac[n]*ifac[m]%mo*ifac[n-m]%mo;}

void work()
{
	scanf("%d %d",&n,&k);
	if (k==1)  puts("1"),exit(0);
	fac[0]=1;
	for (int i=1; i<=n*k; i++)  fac[i]=1LL*fac[i-1]*i%mo;
	ifac[n*k]=qpow(fac[n*k],mo-2);
	for (int i=n*k; i; i--)  ifac[i-1]=1LL*ifac[i]*i%mo;
	f[0][0]=1;
	for (int i=0; i<=n; i++)
		for (int j=i; j<=n; j++)
			{
				if (i<j)  (f[i+1][j]+=f[i][j])%=mo;
				if (j<n)  f[i][j+1]=(f[i][j+1]+1LL*f[i][j]*C(i-1+(k-1)*(j+1),k-2))%mo;
			}
	printf("%d",int(1LL*f[n][n]*fac[n]%mo));
}

int main()
{
	work();
	return 0;
}