TLE '17 Contest 4 P4 - Willson and Target Practice

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Points: 17 (partial)
Time limit: 3.0s
Java 5.0s
Python 10.0s
Memory limit: 512M

Problem types
The poor unsuspecting targets don't see it coming…

Willson the Canada Goose is like any other Canada Goose - he likes to engage in target practice.

There are N unsuspecting targets that Willson can practice on. The i^\text{th} target is located at (x_i,y_i).

Unlike other geese who choose a circular area for target practice, Willson is unique and decides to choose an equilateral triangle with side length K as his area, with the additional constraint that one side of the triangle must be parallel to the line y = 0.

Could you tell Willson the maximum number of targets that could be in such an area?

Note: A target on the perimeter of the triangle is counted.


For all subtasks:

1 \le N \le 20\,000

1 \le K \le 200

All coordinates c satisfy |c| \le 2\,000.

SubtaskPointsAdditional Constraints
320N \le 200
430N \le 2\,000
530No additional constraints

Note 1: There can be multiple targets at the same coordinate.

Note 2: Python users are recommended to submit in PyPy.

Input Specification

The first line of input will contain two integers, N and K.

N lines of input follow. The i^\text{th} line will contain two integers, x_i and y_i.

Output Specification

Output a single integer, the maximum number of targets that can be in an area as described above.

Sample Input

5 3
1 1
2 0
2 4
3 2
3 3

Sample Output




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