Ent Fedya's birthday was coming up, and his friends made a birthday cake
for him. They didn't know how many candles they should put on the cake
because nobody remembered Fedya's age. That is why they just put a very
large number of candles on the cake. When Ent Sasha saw the cake, he got
angry because he had a very good memory and knew that Fedya would become
k years of age. Happily, there were n > k candles on the cake. Since
Fedya's age became known, the ents decided to cut from the cake a convex
polygonal piece of nonzero area that would contain exactly k candles
(counting the cakes inside the piece and on its boundary).
The cake is a 2 · 10^{9} × 2 · 10^{9} mm square. The distance
from each candle to each side of the square is a positive integer number
of millimeters.
Input
The first line contains the integers n and k (1 ≤ k < n ≤
1 000). In the following n lines you are given pairs of integers,
which are the coordinates of the candles. The origin of coordinates is at
the center of the cake and the coordinate axes are parallel to its sides.
All the coordinates are strictly less than 10^{9} in absolute value. It is
guaranteed that no two candles are at the same point.
Output
In the first line output the number m of vertices of the polygon that
should be cut from the cake (3 ≤ m ≤ 10 000). In the following m
lines give the coordinates of the vertices ordered counterclockwise. The
coordinates must be integers not exceeding 10^{9} in absolute value. The
angles at the vertices must not be straight. The lengths of all sides must
be positive. If there are several solutions, output any of them. It is
guaranteed that there exists at least one solution satisfying the above
constraints.
Sample
input  output 

5 3
1 0
1 2
2 1
3 0
3 2
 3
1 0
2 1
1 2

Problem Author: Denis Mukhametianov
Problem Source: Ural Regional School Programming Contest 2011