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Finding Lines

Limits 1s, 512 MB

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 ≤ 105), the number of points the game master hasdrawn;

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

  • n lines each with two integers x and y (0 ≤ x, y ≤ 109), 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

InputOutput
5
55
0 0
10 10
10 0
0 10
3 3
possible

A line with (a tleast) 3 of the points exists.

InputOutput
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.


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