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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.
2 2 2
500 500 2