Time Limit : sec, Memory Limit : KB
English

### Problem Statement

Your friend, Tatsumi, is a producer of Immortal Culture Production in Chiba (ICPC). His company is planning to form a zombie rock band named Gray Faces and cheer Chiba Prefecture up.

But, unfortunately, there is only one zombie in ICPC. So, Tatsumi decided to release the zombie on a platform of Soga station to produce a sufficient number of zombies. As you may know, a zombie changes a human into a new zombie by passing by the human. In other words, a human becomes a zombie when the human and a zombie are at the same point. Note that a zombie who used to be a human changes a human into a zombie too.

The platform of Soga station is represented by an infinitely long line, and Tatsumi will release a zombie at a point with coordinate $x_Z$. After the release, the zombie will start walking in the positive direction at $v_Z$ per second. If $v_Z$ is negative, the zombie will walk in the negative direction at $|v_Z|$ per second.

There are $N$ humans on the platform. When Tatsumi releases the zombie, the $i$-th human will be at a point with coordinate $x_i$ and will start walking in the positive direction at $v_i$ per second. If $v_i$ is negative, the human will walk in the negative direction at $|v_i|$ per second as well as the zombie.

For each human on the platform, Tatsumi wants to know when the human becomes a zombie. Please help him by writing a program that calculates a time when each human on the platform becomes a zombie.

### Input

The input consists of a single test case in the following format.

$N$ $x_Z$ $v_Z$ $x_1$ $v_1$ $\vdots$ $x_N$ $v_N$

The first line consists of an integer $N \, (1 \le N \le 2 \times 10^5)$ which is the number of humans on a platform of Soga station. The second line consists of two integers $x_Z \, (-10^9 \le x_Z \le 10^9)$ and $v_Z \, (-10^9 \le v_Z \le 10^9)$ separated by a space, where $x_Z$ is an initial position of a zombie Tatsumi will release and $v_Z$ is the velocity of the zombie. The $i$-th line in the following $N$ lines contains two integers $x_i \, (-10^9 \le x_i \le 10^9)$ and $v_i \, (-10^9 \le v_i \le 10^9)$ separated by a space, where the $x_i$ is an initial position of the $i$-th human and $v_i$ is the velocity of the human. There is no human that shares their initial position with the zombie. In addition, initial positions of the humans are different from each other.

### Output

The output consists of $N$ lines. In the $i$-th line, print how many seconds it will take for the $i$-th human to become a zombie. If the $i$-th human will never become a zombie, print $-1$ instead. The answer will be considered as correct if the values output have an absolute or relative error less than $10^{-9}$.

### Examples

InputOutput
6
3 1
-5 0
5 0
-4 -3
0 -2
6 -3
2 -1

3.66666666666667
2.00000000000000
-1
6.00000000000000
0.75000000000000
2.00000000000000

5
31415 -926
5358 979
323846 26
-433832 7950
288 -4
-1971 -69

13.67821522309711
95.61812216052499
52.41629112212708
33.76030368763558
38.95682613768962