Xor Grid

Recently Chef invented a new structure that he has called Xor Grid. It is an infinitely large grid G filled with numbers based on these three rules: - G[1, c] = 1 for all c ≥ 1 - G[r, 1] = r for all r ≥ 1 - G[r, c] = G[r - 1, c] xor G[r, c - 1] for all r > 1 and c > 1 Now Chef is wondering, what are the xor sums of all the numbers within some specific rectangles of the Xor Grid? Note Xor sum