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

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