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, 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: $(3 \oplus 7) \& (0 \oplus 7) = 4$ .