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>
#include<cstring>
#include<cstdlib>
#include<algorithm>

using namespace std;

const int MX=2011,md=1000000007;

typedef long long LL;
int dp[MX][MX];
int n,k;
int fac[MX*MX],inv[MX*MX],facinv[MX*MX];

#define C(x,y) ((LL)fac[x]*facinv[y]%md*facinv[(x)-(y)]%md)

void ini(int m){
	inv[1]=1;for(int i=2;i<=m;i++)inv[i]=(LL)inv[md%i]*(md-md/i)%md;
	fac[0]=1;for(int i=1;i<=m;i++)fac[i]=(LL)fac[i-1]*i%md;
	facinv[0]=1;for(int i=1;i<=m;i++)facinv[i]=(LL)facinv[i-1]*inv[i]%md;
}
int main(){
	scanf("%d%d",&n,&k);
	if(k==1)return puts("1"),0;
	ini(n*k);--k;
	for(int i=0;i<=n;i++)
		for(int j=i;j<=n;j++){
			if(!i&&!j)dp[i][j]=1;
			else if(i==j)dp[i][j]=dp[i-1][j];
			else if(!i)dp[i][j]=(LL)dp[i][j-1]*C(j*k-1,k-1)%md;
			else dp[i][j]=((LL)dp[i-1][j]+(LL)dp[i][j-1]*C(j*k-1+i,k-1)%md)%md;
		}
	printf("%lld\n",(LL)fac[n]*dp[n][n]%md);
	return 0;
}