I think you could just have sticked with your first program, and solve it by a coordinate transformation.
3-1 to 1-0 is essentially the same like 2-1 to 0-0
0-0
1-0 1-1
2-0 2-1 2-2
3-0 3-1 3-2 3-3
4-0 4-1 4-2 4-3 4-4
5-0 5-1 5-2 5-3 5-4 5-5
Though you would have ended with more readable code ... nah forget it! ;-)
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