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<iostream>
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cstring>
using namespace std;

typedef long long ll;
const ll maxn=2e3+10,maxnn=maxn*maxn,mod=1e9+7;
ll n,k,fac[maxnn],inv[maxnn];
ll f[maxn][maxn],ans;

ll qpow(ll a,ll n){
	ll res=1;
	while(n){
		if(n&1ll)
			res=res*a%mod;
		a=a*a%mod;
		n>>=1;
	}
	return res;
}

int main(){
	fac[0]=1;
	for(int i=1;i<maxnn;++i)
		fac[i]=fac[i-1]*i%mod;
	inv[maxnn-1]=qpow(fac[maxnn-1],mod-2);
	for(int i=maxnn-1;i;--i)
		inv[i-1]=inv[i]*i%mod;
	scanf("%lld%lld",&n,&k);
	if(k==1){
		puts("1");
		return 0;
	}
	f[1][1]=1;
	for(int i=2;i<=n;++i){
		ll sum=0;
		for(int j=i;j;--j){
			(sum+=f[i-1][j-1])%=mod;
			f[i][j]=sum*fac[i*k-j-1]%mod*inv[k-2]%mod*inv[(i-1)*k-j+1]%mod;
		}
	}
	for(int i=1;i<=n;++i)
		ans+=f[n][i];
	ans=ans%mod*fac[n]%mod;
	printf("%lld\n",ans);
	return 0;
}