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 <iostream>
#include <algorithm>
#define N 2010
#define M 4000000
#define P 1000000007

using namespace std;

typedef long long ll;

int n,k;
ll f[N][N],fac[N*N],inv[N*N];

inline int C(int x,int y){
  if(x<y) return 0;
  return fac[x]*inv[y]%P*inv[x-y]%P;
}

int main(){
  //freopen("1.in","r",stdin);
  //freopen("1.out","w",stdout);
  scanf("%d%d",&n,&k);
  if(k==1) return puts("1"),0;
  fac[0]=inv[0]=inv[1]=1;
  for(int i=1;i<=M;i++) fac[i]=fac[i-1]*i%P;
  for(int i=2;i<=M;i++) inv[i]=(P-P/i)*inv[P%i]%P;
  for(int i=1;i<=M;i++) inv[i]=inv[i]*inv[i-1]%P;
  f[0][0]=1;
  for(int i=1;i<=n;i++)
    for(int j=i;~j;j--){
      f[i][j]=f[i][j+1]%P;
      if(j) (f[i][j]+=f[i-1][j-1]*C(i*k-j-1,k-2))%=P;
    }
  printf("%lld\n",f[n][0]*fac[n]%P);
  return 0;
}