Implement Max Pooling with Indices

Implement max pooling that returns both pooled values and indices for unpooling, a crucial component in CNNs, particularly in encoder-decoder architectures. This operation is essential for preserving spatial information.

Max pooling is a downsampling technique that reduces spatial dimensions by taking the maximum value across each kernel window, defined by $x^2 + y^2 \leq k^2$, where $k$ is the kernel size. The forward pass involves iterating over the input, applying the max pooling operation to each window.

Here are the key steps:

1. Divide the input into overlapping or non-overlapping kernel windows.
2. For each window, find the maximum value and its corresponding index.
3. Store the index for later use in unpooling operations.

This technique is widely used in image segmentation tasks.