Best Triangle

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Given N points on a 2D plane and an integer K, choose 3 distinct points so that the area of the triangle whose vertices are the chosen points does not exceed K/2. If there are multiple such triangles, among all possible triangles choose the one which has maximum area.
Input
First line contains two integers N and K.
Each of the next N lines contains two integers X_{i} and Y_{i}, denoting the coordinates of the ith point.
Output
Output a single integer, the maximum area of a triangle which does not exceed K/2, multiplied by 2. If there's no valid triangle output 1 instead.
Constraints
 3 ≤ N ≤ 3000
 1 ≤ K ≤ 10^{18}
 1 ≤ X_{i},Y_{i} ≤ 10^{9}
 No two points will have same coordinates
 No three points will be collinear
Example 1
Input: 4 7 1 1 5 1 3 3 3 2 Output: 4
Example 2
Input: 3 7 1 1 4 1 1 4 Output: 1
Example 3
Input: 7 1234567890123 1234567 7654321 1111111 2222222 1212121 2323232 3333333 1122334 9292929 2929292 1234456 5654645 5435733 2342134 Output: 755024295480
Explanation
Example case 1. There are 4 triangles in total, and their areas are: 1, 1, 2 and 4. The ones which does not exceed 7/2 are 1, 1 and 2 so the biggest area is 2, and since we are required to multiply the area by 2 before outputting it, it becomes 4.
Example case 2. The only triangle has an area equal to 9/2, which is more than 7/2. So the answer is 1.
Author:  kingofnumbers 
Tester:  mnbvmar 
Editorial  https://discuss.codechef.com/problems/BESTTRI 
Tags  cook81, geometry, kingofnumbers, mediumhard 
Date Added:  18032017 
Time Limit:  7 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.5, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, CLOJ, FS 
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