Description

The National Resource Company (NRC) plans to use satellite to help identify potential mines. To make the problem clear, NRC assumes that the region of interest is a square of land, which can be coordinated as [0, N]*[0, N]. Potential mines are represented as various points in the square. Due to some technical hindrance, the satellite could only detect a region of square of M*M during a single trial, which will give the details of these potential mines within this detecting region. To further simplify the case, NRC announces that its satellite can only detect a region of square, whose vertex locates at the position of integer coordinates, i.e., [A, M+A]*[B, M+B](A and B are integers, and A>=0, B>=0, M+A<=N, M+B<=N); moreover, all the potential mines would never holds an integer coordinate. Therefore, a program should be provided which can determine the detecting region of the satellite to maximize the number of potential mines within the detecting square.

Input

The first line contains the number of test cases T (1 <= T <= 20). Then follow T test cases. For each test case, the total number of points K (0 < K <=10000), N (0 < N <= 1000), M (0 < M <= 100, M <= N) are given in the first line; and the following K lines give the x-coordinate and y-coordinate of the K potential mines. (Notice that the coordinates will be floats)

Output

For each test case, give the optimizing detecting region as print the coordinates of the lower-left vertex of the square in a single line. If more than one choice is possible, give the one that is at the upper-most on the land; if even this cannot turns out a unique solution, give the one that is at the right-most on the land.

1
2 10 3
1.54 1.73
3.12 3.92

1 1

Source

POJ Monthly