Contest Duration: - (local time) (110 minutes) Back to Home
F - Leftmost Ball /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

12，...，N のボールがそれぞれ K 個ずつあります。 高橋君は、これら N×K 個のボールを好きな順番で横一列に並べました。 その後、各色ごとに最も左にあるボールを色 0 へ塗り替えました。

• 1≤N，K≤2,000

N K

2 2

4

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

3 1

1

• (0，0，0)

2 3

14

2000 2000

546381702

### 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.

• 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.

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)

3 1

### Sample Output 2

1

The following 1 sequence is possible:

• (0,0,0)

2 3

14

2000 2000

546381702