You have n points with equal weights and integer coordinated on the coordinate plane. You want to select \(k\) weights and determine the center of mass of these \(k\) weights. You must select the \(k\) weights in such a way that the center of mass has an integer coordinate.

Input format

First line: Two space-separated integers \(n\) and \(k\) denoting the number of points and the number of weights you want to select
Next \(n\) lines: \(i^{th}\) weight contains two integers \(x_i\) and \(y_i\) denoting the coordinates of the \(i^{th}\) weight

Output format

If it is not possible to select \(k\) points that satisfies the provided condition, then print -1. Otherwise, print \(k\) integers of \(i\) indices of the selected weights.

Constraints

\(1 \leq n \leq 10^{5}\\ 1 \leq k \leq 20\\ 1 \leq k \leq n\\ 0 \leq x_i, y_i \leq 10^{9}\)