19139번 - Saddle Point 다국어

bobo has a matrix of size $n \times m$, whose elements are integers from $[1, k]$.

Find out the number of matrices with at least one saddle point, modulo $(10^9+7)$.

Note that a saddle point is a position $(i, j)$ which is both strict maximum of the $i$-th row and $j$-th column.

$3$ integers $n, m, k$ ($1 \leq n, m \leq 500, 1 \leq k \leq 10$).

A single integer denotes the number of matrices.