Problem F. Fence relicts ≡

Author:A. Klenin   Time limit:2 sec
Input file:input.txt   Memory limit:64 Mb
Output file:output.txt  

Statement

The Nearsea region has a large forest, where many relict trees grow. The local government decided to create a reservation park with the area between 0 and S square meters. The park must have a shape of rectangle with the sides parallel to coordinate axises.

Environment activists surveyed the forest and found out that it contained N relict trees located at coordinates (xi, yi), measured in meters.

Find such park location and size that the number of relict trees inside of it or on its boundary is maximum possible.

Input file format

Input file contains integers N S followed by N pairs of integers xi yi.

Output file format

Output file must contain integers xa ya xb yb — coordinates of the two opposite corners of the park. If there is more than one optimal solution, output any of them.

Constraints

1 ≤ N ≤ 500,  − 104 ≤ xi, yi ≤ 104, 1 ≤ S ≤ 109

Sample tests

No. Input file (input.txt) Output file (output.txt)
1 
5 100
0 0  10 0  10 10  0 10  15 10
 
0 0 10 10
2 
3 2
0 0  10 0  20 0
 
0 0 20 0
0.061s 0.009s 13