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 mo 1000000007
using namespace std;
int fac[5001000],nifac[5001000],dp[2010][2010];
int getmi(int a,int x)
{
	int ans=1;
	while (x)
	{
		if (x&1) ans=(long long)ans*a%mo;
		a=(long long)a*a%mo;
		x>>=1;
	}
	return ans;
}
int C(int n,int m){return (long long)fac[n]*nifac[m]%mo*nifac[n-m]%mo;}
int main()
{
	int n,k;scanf("%d%d",&n,&k);
	if (k==1) {puts("1");return 0;}
	fac[0]=1;for (int i=1;i<=n*k;i++) fac[i]=(long long)fac[i-1]*i%mo;
	nifac[n*k]=getmi(fac[n*k],mo-2);
	for (int i=n*k-1;i>=0;i--) nifac[i]=(long long)nifac[i+1]*(i+1)%mo;
	dp[0][0]=1;
	for (int i=0;i<=n;i++)
	for (int j=0;j<=n;j++)
	{
		if (i) dp[i][j]=dp[i-1][j];
		if ((i!=j)&&(j)) dp[i][j]=(dp[i][j]+(long long)dp[i][j-1]*C(i+j*(k-1)-1,k-2))%mo;
	}
	printf("%lld\n",(long long)fac[n]*dp[n][n]%mo);
}