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 <cstdio>
#define IL inline
#define N 2003
#define REP(a,b,c) for(a=b;a<=c;a++)
using namespace std;
typedef long long lol;
const int mod=1e9+7;
IL int qpow(int a,int b){
	int res=1;while(b){if(b&1)res=1LL*res*a%mod;a=1LL*a*a%mod,b>>=1;}return res;
}
int n,k,fac[N*N],inv[N*N],f[N][N];
IL lol C(int n,int m){
	return 1LL*fac[n]*inv[m]%mod*inv[n-m]%mod;
}
IL void work(){
	int i,j=n*k,t;fac[0]=1;
	REP(i,1,j)fac[i]=1LL*fac[i-1]*i%mod;inv[j]=qpow(fac[j],mod-2);
	for(i=j;i;i--)inv[i-1]=1LL*inv[i]*i%mod;
	f[0][0]=1;k--;
	REP(i,0,n)REP(j,i,n){
		t=f[i][j];if(i<j)f[i+1][j]=(f[i+1][j]+t)%mod;
		f[i][j+1]=(f[i][j+1]+t*C(i-1+k*(j+1),k-1))%mod;
	}
	printf("%lld\n",1LL*f[n][n]*fac[n]%mod);
}
int main(){
  scanf("%d%d",&n,&k);
	if(k==1)printf("1");else work();
  return 0;
}