Give a subset that makes $f(x,y) = x - y$ a bijection.

Question

I can't think of a subset that makes $f$ a bijection.

So far, I think the subset should have one constant number, like $(x, n)$ where $n$ is fixed, but this won't cover all positive integers?

$$f : \mathbb{N}^2 \to \mathbb{Z}.$$