Exercise 25, § 1

Let a and b be two coprime integers $> 0$. If a and b are $> 2$, then there exist integers x and y such that ax + by = 1 and $|x| < 1/2$ b, $|y| < 1/2$ a ; moreover the integers x and y are uniquely determined by these conditions. What happens in the case where one of a, b is equal to 2 ?