Encoder Bottleneck

Map each input row to a lower-dimensional code with a single affine transform: $Z=XW+bZ=XW+b$, where X is $n\times dn\backslash times\; d$, W is $d\times md\backslash times\; m$ with and b has length $mm$.

Implement solve(X, W, b).

Returns. Return an $n\times mn\backslash times\; m$ NumPy array.

Examples

Example 1

Input:

solve([[1, 2, 3], [4, 5, 6]], [[1, 0], [0, 1], [1, 1]], [0, 1])

Output:

[[4, 6], [10, 12]]

Example 2

Input:

solve([[1, 1]], [[2], [3]], [1])

Output:

[[6]]