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 mod 1000000007
#define N 2010
inline int Pow(int x,int zs){
	int ret=1;
	for(;zs;zs>>=1,x=x*1ll*x%mod)
		if(zs&1)ret=ret*1ll*x%mod;
	return ret;
}
int f[N][N],n,k,A[10000010],B[10000010];
inline int C(int n,int m){
	if(m>n||m<0)return 0;
	if(n==m||m==0)return 1;
	return A[n]*1ll*B[m]%mod*B[n-m]%mod;
}
int main(){
	n=1e7;
	for(int i=A[0]=1;i<=n;i++)A[i]=A[i-1]*1ll*i%mod;
	B[n]=Pow(A[n],mod-2);
	for(int i=n-1;~i;i--)B[i]=B[i+1]*(i+1ll)%mod;
	scanf("%d%d",&n,&k);
	if(k==1)return puts("1"),0;
	f[0][0]=1;
	for(int i=0;i<=n;i++)
		for(int j=i;j<=n;j++){
			if(i)f[i][j]=f[i-1][j];
			if(j)f[i][j]=(f[i][j]+f[i][j-1]*1ll*C(i+(j-1)*(k-1)+(k-2),k-2))%mod;
		}
	printf("%lld\n",f[n][n]*1ll*A[n]%mod);
	return 0;
}