A12910. Another Filling the Grid

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 $(10^{9} + 7)$ .

In the first example, following $7$ cases are possible.

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