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 int long long
#define Mod 1000000007ll
#define pow ksm
inline int ksm(int a,int x){
	LL ans=1,w=a;
	while(x){
		if(x&1)ans=ans*w%Mod;
		x>>=1;
		w=w*w%Mod;
	}
	return ans;
}
#define MN 4000005
#define mn 2005
int fac[MN],dfac[MN],n,k,f[mn][mn];
inline int C(int n,int m){
	return 1ll*fac[m]*dfac[n]%Mod*dfac[m-n]%Mod;
}
void init(int N){
	fac[0]=1;
	for(int i=1;i<=N;++i)
		fac[i]=fac[i-1]*i%Mod;
	dfac[N]=ksm(fac[N],Mod-2);
	for(int i=N-1;i>=0;--i){
		dfac[i]=(LL)dfac[i+1]*(LL)(i+1)%Mod;
	}
}
signed main(){
	scanf("%lld%lld",&n,&k);
	if(k==1){
		puts("1");
		return 0;
	}
	init(n*k);
	f[0][0]=1;
	for(int i=1;i<=n;++i)
		for(int j=0;j<=i;++j){
			f[i][j]=(f[i][j]+f[i-1][j])%Mod;
			if(j)f[i][j]=(f[i][j]+(f[i][j-1]*(n-j+1)%Mod*C(k-2,n-i+(k-1ll)*(n-j+1ll)-1ll)+Mod))%Mod;	
		}
	printf("%lld",f[n][n]);
	return 0;
}