# Doors

Alex is a circle of radius *R*. Well, life as a circle is not easy. If he were a
point, moving around and passing through doors would be effortless. But now he has to
carefully inspect the surroundings before making every move.

Alex is initially at position (0, *y*_{∞}), where
*y*_{∞} is much bigger than the width of the corridor *w*. Alex
wants to meet Bob, who happens to be living to the far right of the corridor (may as well be
somewhere at (*x*_{∞}, *w*/2), where
*x*_{∞} is much bigger than *ℓ*). The lengths of the two
doors are *ℓ*. It is guaranteed that
*ℓ* ≤ *w*, so that door B will never hit the opposite
side of the wall.

You are given *T* scenarios. In each scenario, the angles *A* and *B*
are given (both are radians in the range [0, π]). Find the largest
*r* ≤ *R* such that when Alex's radius is shrunk to *r*,
he can reach Bob while avoiding the obstacles (walls and doors).

Formally, Alex when shrunk to radius *r* can reach Bob if and only if there exists a
(continuous) curve from (0, *y*_{∞}) to
(*x*_{∞}, *w*/2) such that the minimal distance between a
point on the curve and a point on an obstacle (a wall or a door) is at least *r*. In
particular, if *r* = 0, then Alex will be able to reach Bob.

## Input Specification

The first line of the input consists of three integers, *R*, *ℓ*, and
*w*
(1 ≤ *ℓ*, *w*, *R* ≤ 100
and *ℓ* ≤ *w*). The second line of the input consists of
an integer *T* (1 ≤ *T* ≤ 10 000), the
number of scenarios to follow. Each of the next *T* lines consists of a pair of real
numbers, representing angles *A* and *B* (in radians). The numbers are given
with exactly 4 decimal places.

## Output Specification

For each scenario, output the required answer on a separate line. Your answer will be
accepted if its absolute or relative error (compared to the judge's answer) is at most
10^{–5}.

## Sample Input

`10 6 8`

`4`

`0.0000 0.0000`

`3.1415 0.0000`

`1.0472 0.0000`

`1.0472 1.5708`

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## Output for Sample Input

`0.000000000`

`3.000000000`

`2.598079885`

`1.000000000`

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