Sum Product Segments

A *segment* is a range of **non-negative** integers $L, L + 1, L + 2, \ldots, R$, denoted $[L, R]$ where $L \leq R$. Chef has a set $S$ consisting of **all** segments $[L, R]$ such that either $L + R = X$ or $L\cdot R = Y$. For example, if $X = 5$ and $Y = 6$, then Chef's set is $S = \{[0, 5], [1, 4], [1, 6], [2, 3]\}$. Given the integers $X$ and $Y$, can you help Chef find two non-intersecting