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.

Input

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 $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \lt 2^k$$$) — a sequence of martian numbers.

It is guaranteed that the sum of $$$n$$$ over all testcases does not exceed $$$2 \cdot 10^5$$$.

Output

For each testcase, print three integers $$$i, j, x$$$ ($$$1 \le i, j \le n$$$, $$$i \neq j$$$, $$$0 \le x \lt 2^k$$$). 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.

Note

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

Lisa and the Martians

Examples