This is the easy version of the problem. The only difference is that in this version, you are asked to find a subarray only for the maximum submedian.

You can make hacks only if both versions of the problem are solved.

An integer $v$ is a median of an array $b$ of length $m$ if and only if:

• $v$ is greater than or equal to at least $\lceil \frac{m}{2} \rceil$ elements of the array, and
• $v$ is less than or equal to at least $\lceil \frac{m}{2} \rceil$ elements of the array.

For instance:

• the only median of $[9, 3, 7]$ is $7$,
• the medians of $[5, 3, 7, 9]$ are $5$, $6$, and $7$, and
• the only median of $[2, 2, 2]$ is $2$.

You're given an integer $k$ and an array $a_1, \ldots, a_n$ of integers between $1$ and $n$.

An integer $v$ from $1$ to $n$ is said to be a submedian if there exists at least one pair of indices $(l, r)$ such that

• $1 \leq l \leq r \leq n$,
• $r - l + 1 \geq k$,
• $v$ is a median of the subarray $[a_l, \ldots, a_r]$.

It can be proven that there always exists at least one submedian. Find the maximum submedian $v_\max$ and any corresponding pair of indices $(l, r)$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 50\,000$). The description of the test cases follows.

The first line of each test case contains two integers $n$ and $k$ ($1 \leq k \leq n \leq 300\,000$).

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq n$).

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $300\,000$.

Output

For each test case, output three integers $v_\max$, $l$, and $r$ — the maximum submedian $v_\max$ and the bounds of a subarray of length at least $k$ ($r - l + 1 \geq k$) such that $v_\max$ is one of its medians.

If there are many solutions, you can print any of them.

Note

In the first test case, the subarrays of length at least $k = 3$ are

• $(l = 1, r = 3)$: $[4, 1, 2]$ whose only median is $2$,
• $(l = 2, r = 4)$: $[1, 2, 4]$ whose only median is $2$, and
• $(l = 1, r = 4)$: $[4, 1, 2, 4]$ whose medians are $2$, $3$, and $4$.

In the second test case, one possible output is $(l = 3, r = 4)$ whose medians are $2$ and $3$.

Note that it can be proven that no subarray of length at least $2$ admits $4$ or $5$ as a median.