CF1630B.Range and Partition

Given an array $a$ of $n$ integers, find a range of values $[x, y]$ ( $x \le y$ ), and split $a$ into exactly $k$ ( $1 \le k \le n$ ) subarrays in such a way that:

• Each subarray is formed by several continuous elements of $a$ , that is, it is equal to $a_l, a_{l+1}, \ldots, a_r$ for some $l$ and $r$ ( $1 \leq l \leq r \leq n$ ).
• Each element from $a$ belongs to exactly one subarray.
• In each subarray the number of elements inside the range $[x, y]$ (inclusive) is strictly greater than the number of elements outside the range. An element with index $i$ is inside the range $[x, y]$ if and only if $x \le a_i \le y$ .

Print any solution that minimizes $y - x$ .

The input consists of multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 3 \cdot 10^4$ ) — the number of test cases. Description of the test cases follows.

The first line of each test case contains two integers $n$ and $k$ ( $1 \le k \le n \le 2 \cdot 10^5$ ) — the length of the array $a$ and the number of subarrays required in the partition.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le n$ ) where $a_i$ is the $i$ -th element of the array.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot10^5$ .

For each test case, print $k+1$ lines.

In the first line, print $x$ and $y$ — the limits of the found range.

Then print $k$ lines, the $i$ -th should contain $l_i$ and $r_i$ ( $1\leq l_i \leq r_i \leq n$ ) — the limits of the $i$ -th subarray.

You can print the subarrays in any order.

In the first test, there should be only one subarray, which must be equal to the whole array. There are $2$ elements inside the range $[1, 2]$ and $0$ elements outside, if the chosen range is $[1, 1]$ , there will be $1$ element inside ( $a_1$ ) and $1$ element outside ( $a_2$ ), and the answer will be invalid.

In the second test, it is possible to choose the range $[2, 2]$ , and split the array in subarrays $(1, 3)$ and $(4, 4)$ , in subarray $(1, 3)$ there are $2$ elements inside the range ( $a_2$ and $a_3$ ) and $1$ element outside ( $a_1$ ), in subarray $(4, 4)$ there is only $1$ element ( $a_4$ ), and it is inside the range.

In the third test, it is possible to choose the range $[5, 5]$ , and split the array in subarrays $(1, 4)$ , $(5, 7)$ and $(8, 11)$ , in the subarray $(1, 4)$ there are $3$ elements inside the range and $1$ element outside, in the subarray $(5, 7)$ there are $2$ elements inside and $1$ element outside and in the subarray $(8, 11)$ there are $3$ elements inside and $1$ element outside.