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
const int N=2100,mod=1000000007;
int n,K;
int jc[N*N],njc[N*N],f[N][N];
int qpow(int x,int y)
{
	int ret=1;
	while(y)
	{
		if(y&1)ret=(ll)ret*x%mod;
		x=(ll)x*x%mod;y>>=1;
	}
	return ret;
}
void init()
{
	jc[0]=njc[0]=1;
	for(int i=1;i<=n*K;i++)jc[i]=(ll)jc[i-1]*i%mod;
	njc[n*K]=qpow(jc[n*K],mod-2);
	for(int i=n*K-1;i>=1;i--)njc[i]=(ll)njc[i+1]*(i+1)%mod;
}
int C(int x,int y){return (ll)jc[x]*njc[y]%mod*njc[x-y]%mod;}
int main()
{
	//freopen("tt.in","r",stdin);
	scanf("%d%d",&n,&K);
	if(K==1)return puts("1"),0;
	init();
	f[0][0]=1;
	for(int i=0;i<=n;i++)
		for(int j=i;j<=n;j++)
		{
			if(i<j)(f[i+1][j]+=f[i][j])%=mod;
			if(j!=n)(f[i][j+1]+=(ll)f[i][j]*C((K-1)*(j+1)+i-1,K-2)%mod)%=mod;
		}
	printf("%d\n",(ll)f[n][n]*jc[n]%mod);
	return 0;
}