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.