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;
#define LL long long
#define C(n,m) ((LL)fac[n]*ifac[m]%mo*ifac[(n)-(m)]%mo)

const int maxn=2010;
const int mo=1e9+7;
const int N=4000000;

int n,k,dp[maxn][maxn];
int fac[maxn*maxn],ifac[maxn*maxn];

int power(int x,int k)
{
	int res=1;
	while (k)
	{
		if (k&1) res=(LL)res*x%mo;
		x=(LL)x*x%mo;
		k>>=1;
	}
	return res;
}

int main()
{
#ifdef h10
	freopen("F.in","r",stdin);
	freopen("F.out","w",stdout);
#endif
	int i,j;
	fac[0]=1;
	for (i=1;i<=N;i++)
		fac[i]=(LL)fac[i-1]*i%mo;
	ifac[N]=power(fac[N],mo-2);
	for (i=N;i>=1;i--)
		ifac[i-1]=(LL)ifac[i]*i%mo;
	scanf("%d%d",&n,&k);
	if (k==1) {puts("1"); return 0;}
	dp[0][0]=1;
	for (i=0;i<=n;i++)
	for (j=0;j<=n;j++)
		if (dp[i][j])
		{
			(dp[i+1][j]+=dp[i][j])%=mo;
			if (i>j)
				(dp[i][j+1]+=(LL)dp[i][j]*C((n-j)*k-i+j-1,k-2)%mo)%=mo;
		}
	printf("%lld\n",(LL)dp[n][n]*fac[n]%mo);
}