F. Lisa and the Martianstime limit per test3 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputLisa was kidnapped by martians! It okay, because she has watched a lot of TV shows about aliens, so she knows what awaits her. Let's call integer martian if it is a non-negative integer and strictly less than 2^k, for example, when k = 12, the numbers 51, 1960, 0 are martian, and the numbers \pi, -1, \frac{21}{8}, 4096 are not.The aliens will give Lisa n martian numbers a_1, a_2, \ldots, a_n. Then they will ask her to name any martian number x. After that, Lisa will select a pair of numbers a_i, a_j (i \neq j) in the given sequence and count (a_i \oplus x) \& (a_j \oplus x). The operation \oplus means Bitwise exclusive OR, the operation \& means Bitwise And. For example, (5 \oplus 17) \& (23 \oplus 17) = (00101_2 \oplus 10001_2) \& (10111_2 \oplus 10001_2) = 10100_2 \& 00110_2 = 00100_2 = 4.Lisa is sure that the higher the calculated value, the higher her chances of returning home. Help the girl choose such i, j, x that maximize the calculated value.InputThe first line contains an integer t (1 \le t \le 10^4) — number of testcases.Each testcase is described by two lines.The first line contains integers n, k (2 \le n \le 2 \cdot 10^5, 1 \le k \le 30) — the length of the sequence of martian numbers and the value of k.The second line contains n integers a_1, a_2, \ldots, a_n (0 \le a_i < 2^k) — a sequence of martian numbers.It is guaranteed that the sum of n over all testcases does not exceed 2 \cdot 10^5.OutputFor each testcase, print three integers i, j, x (1 \le i, j \le n, i \neq j, 0 \le x < 2^k). The value of (a_i \oplus x) \& (a_j \oplus x) should be the maximum possible.If there are several solutions, you can print any one.ExampleInput
105 43 9 1 4 133 11 0 16 12144 1580 1024 100 9 134 37 3 0 43 20 0 12 412 29 46 14 9 4 4 4 5 10 22 11 02 411 49 42 11 10 1 6 9 11 0 5Output
1 3 14
1 3 0
5 6 4082
2 3 7
1 2 3
1 2 15
4 5 11
1 2 0
1 2 0
2 7 4
NoteFirst testcase: (3 \oplus 14) \& (1 \oplus 14) = (0011_2 \oplus 1110_2) \& (0001_2 \oplus 1110_2) = 1101_2 = 1101_2 \& 1111_2 = 1101_2 = 13.Second testcase: (1 \oplus 0) \& (1 \oplus 0) = 1.Third testcase: (9 \oplus 4082) \& (13 \oplus 4082) = 4091.Fourth testcase: (3 \oplus 7) \& (0 \oplus 7) = 4.
105 43 9 1 4 133 11 0 16 12144 1580 1024 100 9 134 37 3 0 43 20 0 12 412 29 46 14 9 4 4 4 5 10 22 11 02 411 49 42 11 10 1 6 9 11 0 5
1 3 14 1 3 0 5 6 4082 2 3 7 1 2 3 1 2 15 4 5 11 1 2 0 1 2 0 2 7 4 
['bitmasks', 'greedy', 'math', 'strings', 'trees', '*1800']