21537_HarmoniousMatrices

Call an m × n matrix of bits "harmonious" if every cell in it has an even number of 1 bits as neighbors. A cell is a neighbor of itself, and also to the cells above, below, left, and right (if they exist). So the number of neighbors of a cell is at most five, but could be less, depending on where it is. The following is an harmonious 4 × 4 square of bits:

0 1 0 01 1 1 00 0 0 11 1 0 1

The task is to write a program which takes as input m and n, and produces an harmonious matrix of m rows and n columns of bits. The solution should avoid the all-zero matrix (if possible).

The input will begin with a number Z ≤ 40 on a line by itself. This is followed by Z lines, each of which contains two space-separated positive integers m and n, each of which will be at most 40.

For each input instance, the output will be an m × n harmonious matrix of 0s and 1s. The matrix should be non-zero if possible.

2
4 4
1 6

0 1 0 0
1 1 1 0
0 0 0 1
1 1 0 1
0 0 0 0 0 0