Problem Statement

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.

Sample Input 1

2 2

Sample Output 1

4

The following 4 sequences are possible:

  • (0,1,0,2)
  • (0,0,1,2)
  • (0,2,0,1)
  • (0,0,2,1)

Sample Input 2

3 1

Sample Output 2

1

The following 1 sequence is possible:

  • (0,0,0)

Sample Input 3

2 3

Sample Output 3

14

Sample Input 4

2000 2000

Sample Output 4

546381702