Finding Lines

Annabel and Richard like to invent new games and play against each other. One day Annabel has a new game for Richard. In this game there is a game master and a player. The game master draws $n$ points on a piece of paper. The task for the player is to find a straight line, such that at least $p$ percent of the points lie exactly on that line. Richard and Annabel have very good tools for measurement and drawing. Therefore they can check whether a point lies exactly on a line or not. If the player can find such a line then the player wins. Otherwise the game master wins the game.

There is just one problem. The game master can draw the points in a way such that it is not possible at all to draw a suitable line. They need an independent mechanism to check whether there even exists a line containing at least $p$ percent of the points, i.e., $\lceil n \cdot p/100 \rceil$ points. Now it is up to you to help them and write a program to solve this task.

Input

The input consists of:

• one line with one integer $n$ ($1 ≤ n ≤ 10^5$), the number of points the game master has drawn;

• one line with one integer $p$ ($20 ≤ p ≤ 100$), the percentage of points which need to lie on the line;

• n lines each with two integers $x$ and $y$ ($0 ≤ x, y ≤ 10^9$), the coordinates of a point.

No two points will coincide.

Output

Output one line containing either "possible" if it is possible to find a suitable line or "impossible" otherwise.

Samples

Input	Output
5 55 0 0 10 10 10 0 0 10 3 3	possible
A line with (at least) 3 of the points exists.

Input	Output
5 45 0 0 10 10 10 0 0 10 3 4	impossible
No line with at least 3 points exists.

This NWERC 2014 problem is licensed under the CC BY-SA 3.0 license.

You can find the original problem on the NWERC website.