Quadratic Permutation High

Consider a permutation of numbers from $a$ to $b$. We call it a quadratic permutation if, for each element, the sum of the element and the element that replaces it in the permutation is a perfect square. More precisely, a quadratic permutation is defined as a bijection $p$ of the set of integers \{ a, a+1, \ldots, b \} onto itself, such that for any integer $i$, the condition i + p(i) = j^2 holds for some integer $j$. Given $a$ and $b$, your task is to find a quadratic permutation.

Constraints

• $a$, $b$ are integers.

• 0 \leq a \leq 100

• 0 \leq b \leq 100000

• a \leq b