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., $\left\lceil n\cdot p/100 \right\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 $n$ ($1\le n\le 10^5$), 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

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

\includegraphics[width=0.30\textwidth ]{sample1.pdf}
(a) Sample input 1: A line with (at least) 3 of the points exists.
\includegraphics[width=0.30\textwidth ]{sample2.pdf}
(b) Sample input 2: No line with at least 3 points exists.
Figure 1: Illustration of the sample inputs
Sample Input 1 Sample Output 1
5
55
0 0
10 10
10 0
0 10
3 3
possible
Sample Input 2 Sample Output 2
5
45
0 0
10 10
10 0
0 10
3 4
impossible