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. ceil(n * p / 100) points. Now it is up to you to help them and write a program to solve this task.
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.
