Migrated from Lutece 1117 Finding Lines

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Description

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., $⌈ n⋅p/100⌉$ 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

5
55
0 0
10 10
10 0
0 10
3 3

possible

5
45
0 0
10 10
10 0
0 10
3 4

impossible

Note

Resources

2015 UESTC ACM Summer Training Team Selection (3)