Quadratic Permutation Junior#4574
Consider a permutation of numbers from to . We will 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 specifically, a quadratic permutation is defined as a bijection of the set of integers from to onto itself, such that for any integer , the equation i + p(i) = j^2 holds for some integer . Given and , your task is to find a quadratic permutation.
Constraints
, are integers such that 0 \leq a \leq b \leq 20.
The input consists of a single line containing the numbers and .
Output b - a + 1 numbers that represent the values of for all from to , where is a quadratic permutation. If no such permutation exists for the given and , output the single number .
Example 1