You are given an array A containing N integers. The following functions are defined for this array:

• $f_1(l,r) =$XOR of the first M smallest elements in the subarray from l to r, $l \le r$ and $r-l+1 \ge M$
• $f_2(l,r) =$XOR of the first P largest elements in the subarray from l to r, $l \le r$ and $r-l+1 \ge P$
• $f_3(l,r) = f_1(l,r) \space \& \space f_2(l,r)$, $l \le r$

Write a program to find l and r such that $f_3(l,r)$ is maximum. If there are several values of l and r for which $f_3(l,r)$ is maximum, return the one having the largest length. If multiple values still exist, return the one with the smallest l.

Input format

• First line: T (number of test cases)
• First line in each test case: Three space-separated integers denoting N,M, and P respectively.
  
• Second line in each test case: N space-separated integers (denoting the array A)

Output format

For each test case, print three space-separated integers denoting l, r, and $f_3(l,r)$.

Constraints

$1 \le T \le 5$
$1 \le N \le 2000$
$1 \le M, P \le N$
$0 \le A[i] \le 10^9$