2D Max Pooling

Given matrix $A$ of shape $h \times w$ stored in row-major order and a square pooling window of side $k$, produce matrix $B$ of shape $\lfloor h/k \rfloor \times \lfloor w/k \rfloor$ such that

The stride equals $k$ so the windows do not overlap. If $h$ or $w$ is not divisible by $k$, the trailing rows or columns are discarded.

Input

• A - input matrix of shape [h][w] stored in row-major order.
• h - the number of rows in A.
• w - the number of columns in A.
• kernel_size - the side length $k$ of the square pooling window (also the stride).

Output

• B - pooled matrix of shape [h/k][w/k] where each cell holds the maximum value of its corresponding $k \times k$ region of A.