Person in Charge

• 035966_L3

Problem Description

Given that the $nm$ vertices of a simple $nm$-gon form exactly an $n \times m$ square grid (each small square has side length $1$), find the average area of all such polygons.

Input Format

This problem contains multiple test cases.

The first line contains a positive integer $T\ (1 \le T \le 400)$, indicating the number of test cases.

The following $T$ lines each contain two positive integers $n,m\ (6 \le n,m \le 25)$.

Output Format

For each test case, output a line with a $3$-decimal-place number representing the answer. No errors are allowed.

Samples

1
6 6

17.000