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.
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 one line containing either “possible” if it is possible to find a suitable line or “impossible” otherwise.
(a) Sample input 1: A line with (at least) 3 of the points exists. |
(b) Sample input 2: No line with at least 3 points exists. |
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 |
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5 45 0 0 10 10 10 0 0 10 3 4 |
impossible |