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>

int f[2001][2001],n,k,invmul[4000001],_mul[4000001];
const int P=1000000007;
inline int mul(const int &a,const int &b){return 1ll*a*b%P;}
inline int add(int a,const int &b){a+=b;return(a>=P)?a-P:a;}
inline int sub(int a,const int &b){a-=b;return (a<0)?a+P:a;}
inline int C(const int &n,const int &m){return mul(mul(_mul[n],invmul[m]),invmul[n-m]);}
int main(){
	scanf("%d%d",&n,&k);
	if(k==1){
		puts("1");
		return 0;
	}
	_mul[0]=_mul[1]=invmul[0]=invmul[1]=1;
	for(int i=2;i<=n*k;i++)_mul[i]=mul(_mul[i-1],i);
	for(int i=2;i<=n*k;i++)invmul[i]=mul(P-P/i,invmul[P%i]);
	for(int i=2;i<=n*k;i++)invmul[i]=mul(invmul[i-1],invmul[i]);
	f[0][0]=1;
	for(int i=1;i<=n;i++){
		f[i][0]=1;
		for(int j=1;j<=i;j++)
			f[i][j]=add((j<i)?f[i-1][j]:0,mul(f[i][j-1],C(n*k-i-(j-1)*(k-1)-1,k-2)));
	}
	printf("%d ",mul(f[n][n],_mul[n]));
}