[AGC002F] Leftmost Ball
题意翻译
给你 $n$ 种颜色的球，每个球有 $k$ 个，把这 $n\times k$ 个球排成一排，把每一种颜色的最左边出现的球涂成白色(初始球不包含白色)，求有多少种不同的颜色序列，答案对 $10^9+7$ 取模。
翻译提供自[@asfasfasfad](https://www.luogu.org/space/show?uid=6300)
题目描述
[problemUrl]: https://agc002.contest.atcoder.jp/tasks/agc002_f
输入输出格式
输入格式
The input is given from Standard Input in the following format:
```
$ N $ $ K $
```
输出格式
Print the number of the possible sequences of the colors of the balls after painting, modulo $ 10^9+7 $ .
输入输出样例
输入样例 #1
2 2输出样例 #1
4输入样例 #2
3 1输出样例 #2
1输入样例 #3
2 3输出样例 #3
14输入样例 #4
2000 2000输出样例 #4
546381702说明
### 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\ \leq\ N,K\ \leq\ 2,000 $
### Sample Explanation 1
The following $ 4 $ sequences are possible:
- $ (0,1,0,2) $
- $ (0,0,1,2) $
- $ (0,2,0,1) $
- $ (0,0,2,1) $
### Sample Explanation 2
The following $ 1 $ sequence is possible:
- $ (0,0,0) $