Everyone loves short problem statements.

Given a function $ f(x) $ find its minimum value over the range $ 0 < x < π/2$
f(x) = ( x^{2} + b*x + c ) / sin( x )

------ Input: ------

First-line will contain $T$, the number of test cases. Then the test cases follow.
Each test case contains a single line of input, two real numbers $b, c$.

------ Output: ------
For each test case, output the minimum value of $ f(x) $ over the given range. Absolute error of $10^{-6}$ is allowed.

------ Constraints ------
$1 ≤ T ≤ 100000$
$1 ≤ b,c ≤ 20$

------ Sample Input: ------
1
2 2

------ Sample Output: ------
5.8831725615

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见题面