Convoluted Expression

Description

One of your engineer friends says that he has to do a lot of long tedious calculations and that he would appreciate it if you wrote a program to do it for him. He gives you the expression below.

$\Huge A=\frac{\log_{10}\left(x^{\sqrt{y}}\right)}{x+y+\cos(xy)}$

The expression is so convoluted and seemingly irrelevant that you begin to wonder if your friend is really an engineer. You decide to the write the program anyway.

Note: The cosine function in this expression uses degrees.

Input

The first line contains a single integer $N$, the number of calculations to be done. $N$ lines follow, each with two integers, $x$ and $y$, respectively. You may assume that no calculation will result in an undefined value.

Output

For each test case, output a line containing $A$ rounded to 8 decimal places.

Sample Input

3
32 2
5 1
3 4

Sample Output

0.06180906
0.09990717
0.11960703