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 $(10^{9} + 7)$. [Image] These are the examples of valid and invalid grid when $n=k=2$.

-----Input-----

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

-----Output-----

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

-----Examples-----

Input 2 2

Output 7

Input 123 456789

Output 689974806

-----Note-----

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

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