CF1851F Lisa and the Martians

Lisa 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](http://tiny.cc/xor_wiki), 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.

The 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 $ .

For 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.

First 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 $ .