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 RI register int
const int mod=1000000007,N=2005,M=4000005;
int n,K,f[N][N],fac[M],ni[M];
int qm(int x) {return x>=mod?x-mod:x;}
int ksm(int x,int y) {
	int re=1;
	for(;y;y>>=1,x=1LL*x*x%mod) if(y&1) re=1LL*re*x%mod;
	return re;
}
void prework() {
	fac[0]=1;for(RI i=1;i<=n*K;++i) fac[i]=1LL*fac[i-1]*i%mod;
	ni[n*K]=ksm(fac[n*K],mod-2);
	for(RI i=n*K-1;i>=0;--i) ni[i]=1LL*ni[i+1]*(i+1)%mod;
}
int C(int d,int u) {return 1LL*fac[d]*ni[u]%mod*ni[d-u]%mod;}
int main()
{
	scanf("%d%d",&n,&K);
	if(K==1) {puts("1");return 0;}
	prework();--K;
	f[0][0]=1;
	for(RI i=1;i<=n;++i) {
		for(RI j=0;j<=i;++j) {
			if(j) f[i][j]=f[i][j-1];
			f[i][j]=qm(f[i][j]+1LL*f[i-1][j]*C(i*K+j-1,K-1)%mod);
		}
	}
	printf("%lld\n",1LL*f[n][n]*fac[n]%mod);
    return 0;
}