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 LL long long
using namespace std;
const int mod=1e9+7;
struct Combin{
	#define N 4000005
	int fac[N],rv[N],facrv[N];
	Combin(){
		fac[0]=rv[1]=facrv[0]=1;
		for(int i=2;i<N;i++) rv[i]=((-(LL)(mod/i)*rv[mod%i]%mod)+mod)%mod;
		for(int i=1;i<N;i++) fac[i]=(LL)fac[i-1]*i%mod;
		for(int i=1;i<N;i++) facrv[i]=(LL)facrv[i-1]*rv[i]%mod;
	}
	int C(int r1,int n1){
		if(r1>n1) return 0;
		return fac[n1]*(LL)facrv[r1]%mod*facrv[n1-r1]%mod;
	}
	#undef N
}C;
int n,k;
int dp[2][2005];
int main(){
	scanf("%d%d",&n,&k);
	if(k==1) return puts("1"),0;
	int now=0;
	for(int i=0;i<=n;i++){
		memset(dp[now],0,sizeof(dp[0]));
		for(int j=i;j<=n;j++){
			if(j==i) dp[now][j]=i==0? 1:dp[now^1][j];
			else dp[now][j]=(dp[now^1][j] + dp[now][j-1]*1LL*C.C(k-2,k-2+i*k+(j-i-1)*(k-1)))%mod;
		}
		now^=1;
	}
	cout<<dp[now^1][n]*1LL*C.fac[n]%mod<<endl;
	return 0;
}