Find K Closest Points to the Origin

Given a list of n points with integer coordinates, your task is to find the k points closest to the origin (0, 0). The distance is calculated using the Euclidean distance formula: \(\sqrt{x^2 + y^2}\). In the event of a tie (i.e. two points having the same distance), sort the points by their x-coordinate and then by their y-coordinate.

If k exceeds the total number of points, output all points sorted according to the criteria above. If k equals 0, output nothing.

inputFormat

The input is read from stdin and has the following format:

1. The first line contains two integers, n (the number of points) and k (the number of closest points to find).
2. The next n lines each contain two space-separated integers representing the x and y coordinates of a point.

outputFormat

The output is written to stdout and should contain exactly k lines (or all points if k exceeds n). Each line must contain two integers representing the x and y coordinates of one of the closest points to the origin, sorted in increasing order of their Euclidean distance. For points with the same distance, they must be sorted by x-coordinate, then by y-coordinate.

## sample

4 2
1 3
-2 2
5 8
0 1

0 1
-2 2

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