[Solution] Pythagorean Pair CodeChef Solution

Problem

Chef has an integer $N$. It is known that the largest odd divisor of $N$ does not exceed $10^5$.

Determine two non-negative integers $A$ and $B$ such that $A^2 + B^2 = N$, or report that no such pair exists.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of a single integer $N$.

Output Format

For each test case, output space-separated $A$ and $B$ such that $A^2 + B^2 = N$ or $-1$ if no such pair exists.

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Explanation:

Test case $1$: A possible pair $(A, B)$ such that $A^2 + B^2 = N$ is $(8, 6)$. Here, $8^2 + 6^2 = 64+36 = 100$.

Test case $2$: There is no pair $(A, B)$ such that $A^2 + B^2 = N$.

Test case $3$: A possible pair $(A, B)$ such that $A^2 + B^2 = N$ is $(2, 3)$. Here, $2^2 + 3^2 = 4+9 = 13$

Test case $4$: A possible pair $(A, B)$ such that $A^2 + B^2 = N$ is $(0, 2)$. Here, $0^2 + 2^2 = 0+4 = 4$.