30171번 - Another Filling the Grid 다국어

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