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Description

In a boring afternoon, Tom and Marie are two boring people playing a boring game.

The rules of the game is easy.

At first Tom will drew a boring circle and the boring circle's area is $x$.

In each round, Mary will be in the circle and draw a point randomly.And Tom will preserve the maximal circular portion without the point.If the area of the circle is less than $y$,the game will end.

So what's the expectation of the numbers of round played?

Input

First line of input consists of a single integer containing the number of test cases $T$ ( equal to around $500000$)

each of the following $T$ lines contain two integer $x$,$y$.($0<y\le x\le 3y<1000000000$)

Output

ans the absolute error should be less than $10^{-6}$.

Samples

2
2 1
1 1

2.591439944260
1.000000000000

Resources

IEEEXTREME Programming Competition