Another Filling the Grid

You have an $n \times n$ square grid and an integer $k$. Write an integer in each cell so that all of the following conditions hold.

• Every number in the grid is between 1 and $k$, inclusive.
• The minimum of the $i$-th row is 1 ($1 \le i \le n$).
• The minimum of the $j$-th column is 1 ($1 \le j \le n$).

Count the ways to fill the grid. The answer can be very large, so print it modulo $(10^{9} + 7)$.

The figure shows valid and invalid grids 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 $(10^{9} + 7)$.

When $n=k=2$, there are 7 valid grids.