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.

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.

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 $10^{-9}$.

Input | Output |
---|---|

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 |