Farmer John is planning to build N (2 <= N <= 50,000) square fenced-in pastures on his farm, each of size exactly K x K (1 <= K <= 1,000,000). Pasture i is centered at point (x_i, y_i) with integer coordinates in the range -1,000,000...1,000,000. However, in his haste to complete his plans, FJ realizes that he may have accidentally placed two pastures in locations that overlap (by overlap, this means the two pastures share a positive area in common). No two pastures share the exact same center point.</p>

Given the locations of each of the planned square pastures, please help FJ compute the area shared by the two overlapping pastures. Output zero if no two squares overlap, and -1 if overlap occurs between more than a single pair of pastures.

입력 형식

• Line 1: Two space-separated integers, N and K. K is guaranteed to be even.
• Lines 2..1+N: Line i+1 contains the integers x_i and y_i, describing the center of the ith pasture.

출력 형식

• Line 1: The area shared by the two overlapping squares. Output zero if no two squares overlap, and -1 if overlap occurs between more than a single pair of pastures.

예제 입력

4 6
0 0
8 4
-2 1
0 7

예제 출력

20

힌트

Input Details

There are 4 squares, each of size 6 x 6. The first square is centered at (0,0), and so on.

Output Details

Pastures #1 and #3 overlap in 20 units of area.