Another Filling the Grid

给定一个 $n\times n$ 的矩阵，用 $1\sim k$ 的数填充，每行每列最小值均为 $1$，问有多少填法，对 $10^9+7$ 取模。 $1\le n\le 250,1\le k\le 10^9$。

You have $ n \times n $ square grid and an integer $ k $ . Put an integer in each cell while satisfying the conditions below. - All numbers in the grid should be between $ 1 $ and $ k $ inclusive. - Minimum number of the $ i $ -th row is $ 1 $ ( $ 1 \le i \le n $ ). - Minimum number of the $ j $ -th column is $ 1 $ ( $ 1 \le j \le n $ ). Find the number of ways to put integers in the grid. Since the answer can be very large, find the answer modulo $ (10^{9} + 7) $ .  These are the examples of valid and invalid grid when $ n=k=2 $ .

The only line contains two integers $ n $ and $ k $ ( $ 1 \le n \le 250 $ , $ 1 \le k \le 10^{9} $ ).

Print the answer modulo $ (10^{9} + 7) $ .

2 2

7

123 456789

689974806

In the first example, following $ 7 $ cases are possible. In the second example, make sure you print the answer modulo $ (10^{9} + 7) $ .