You are famous after you solve math problems of your brothers. Now, one of your neighbor needs to count the number of intersecting circles (adjacent, intersecting or overlapping). The two circles are intersecting if the distance between them is smaller than or equal to the sum of the two radii.

Question: You are given the coordinates and radius of n circles. Find the top k circles which intersect with the most number of circles.

Input specification: First, you will be given two integers: the number of circles (n) and the number of top intersecting circles to list (m). The following n lines contain three integers: center coordinate (x,y) and the radius where 1 ≤ m ≤ n ≤ 5,000.

Output specification: Show k integers (orders of top m circles). If the two circles intersecting with the same number of circles, first show the one which appears before the other.

Explanation: There are 6 circles given, and the top 2 circles will be listed.