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., $\lceil \frac{n\cdot p}{100e}\rceil$ points. Now it is up to you to help them and write a program to solve this task.

Input Specification

The input consists of:

• one line with one integer $n$ $(1\le n\le {10}^5)$, the number of points the game master has drawn;
• one line with one integer $p$ $(20\le p\le 100)$, the percentage of points which need to lie on the line;
• $n$ lines each with two integers $x$ and $y$ $(0\le x,y\le {10}^9)$, the coordinates of a point.

No two points will coincide.

Output Specification

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

Sample Input 1

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

Sample Output 1

possible

Explanation for Sample 1

A line with (at least) $3$ of the points exists.

Sample Input 2

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

Sample Output 2

impossible

Explanation for Sample 2

No line with at least $3$ points exists.