Ankara Messi

It is Argentina vs Croatia in the football world cup semifinal of 2022 in a parallel universe.

The football field can be considered as an infinite $2$- dimensional plane. Lionel Messi of Argentina has the ball. He is at coordinate $(x,0)$. Joško Gvardiol, a defender of Croatia is at $(x-1,0)$. At any moment, Gvardiol runs directly towards Messi at speed $1$ unit per second. Messi knows the movement strategy of Gvardiol. Messi himself has a maximum speed of $v$ unit per second.

Gvardiol will tackle Messi if the distance between them becomes strictly less than $1$ unit. Gvardiol has a choice to foul Messi at a moment when Messi moves from a position which is more than 1 unit away to a position which is exactly $1$ unit away from Gvardiol. A dribble is a path on the field which Messi can take to move to coordinate $(0,0)$ without getting tackled or fouled.

Messi does not know if Gvardiol intends to foul or not. So to be safe, he plans his dribble assuming that Gvardiol will foul him given the chance.

A dribble $X$ is called boring if Messi can make a dribble shorter than $X$ if he knows beforehand that Gvardiol won’t foul.

Messi wants to know the length of the shortest dribble which is not boring. It can be proved that such a dribble exists under the given constraints.

Input

First line contains an integer $T$ $(1 \leq T \leq 5 \times 10^4 )$, the number of test cases.
Each of the next $T$ lines contains two space separated floating point numbers $x$ $(2 \leq x \leq 100)$ and $v$ $(1 \lt v \leq 100)$. Both numbers have $5$ digits after decimal.

Output

Print the answer for each case in a separate line. Your answer is considered correct if its absolute or relative error does not exceed $10^{-6}$. Formally, let your answer be $A$, and the jury's answer be $B$. Your answer is accepted if and only if $\frac{\lvert A-B \rvert}{\max(1, B)}$ $\leq$ $10^{-6}$.

Sample

Input	Output
2 2.50000 2.60000 10.00000 100.00000	4.374718737669 10.637610774649