Set Matrix Zeroes

Problem

Given a m x n matrix, if an element is 0, set its entire row and column to 0. Do it in place.

Example

Given a matrix

[
  [1,2],
  [0,3]
],

return

[
  [0,2],
  [0,0]
]

Challenge

Did you use extra space?

A straight forward solution using O(mn) space is probably a bad idea.

A simple improvement uses O(m + n) space, but still not the best solution.

Could you devise a constant space solution?