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=2005,mod=1000000007;
int n,k,dp[N][N],fac[N*N],ifac[N*N];
int pw(int a,int b){int r=1;for(;b;b>>=1,a=1ll*a*a%mod)if(b&1)r=1ll*r*a%mod;return r;}
int C(int a,int b){return a<0||b<0||a<b?0:1ll*fac[a]*ifac[b]%mod*ifac[a-b]%mod;}
int main()
{
	for(int i=fac[0]=1;i<N*N;i++)fac[i]=1ll*fac[i-1]*i%mod;
	ifac[N*N-1]=pw(fac[N*N-1],mod-2);
	for(int i=N*N-1;i;i--)ifac[i-1]=1ll*ifac[i]*i%mod;
	scanf("%d%d",&n,&k);
	if(k==1){puts("1");return 0;}
	dp[0][0]=1;
	for(int i=0;i<=n;i++)for(int j=0;j<=i;j++)
	{
		if(i)dp[i][j]=(dp[i][j]+dp[i-1][j])%mod;
		if(j)dp[i][j]=(dp[i][j]+1ll*dp[i][j-1]*C(n*k-i-(j-1)*(k-1)-1,k-2))%mod;
	}
	printf("%d\n",1ll*dp[n][n]*fac[n]%mod);
	return 0;
}