Mathematical Curiosity

You are given two integers $n$ and $m$. Among the integer pairs $(a, b)$ with $0 < a < b < n$, count the pairs for which $\frac{a^2 + b^2 + m}{ab}$ is an integer.

The first line holds the number of test cases $T$. Each of the next $T$ lines holds one test case, with $n$ and $m$ separated by a space. Both numbers are greater than $0$ and at most $100$.

For each test case, print the number of pairs $(a, b)$ that satisfy the condition, one per line.