CF1676F.Longest Strike

Given an array $a$ of length $n$ and an integer $k$ , you are tasked to find any two numbers $l$ and $r$ ( $l \leq r$ ) such that:

• For each $x$ $(l \leq x \leq r)$ , $x$ appears in $a$ at least $k$ times (i.e. $k$ or more array elements are equal to $x$ ).
• The value $r-l$ is maximized.

If no numbers satisfy the conditions, output -1.

For example, if $a=[11, 11, 12, 13, 13, 14, 14]$ and $k=2$ , then:

• for $l=12$ , $r=14$ the first condition fails because $12$ does not appear at least $k=2$ times.
• for $l=13$ , $r=14$ the first condition holds, because $13$ occurs at least $k=2$ times in $a$ and $14$ occurs at least $k=2$ times in $a$ .
• for $l=11$ , $r=11$ the first condition holds, because $11$ occurs at least $k=2$ times in $a$ .

A pair of $l$ and $r$ for which the first condition holds and $r-l$ is maximal is $l = 13$ , $r = 14$ .

The first line of the input contains a single integer $t$ ( $1 \le t \le 1000$ ) — the number of test cases. The description of test cases follows.

The first line of each test case contains the integers $n$ and $k$ ( $1 \le n \le 2 \cdot 10^5$ , $1 \leq k \leq n$ ) — the length of the array $a$ and the minimum amount of times each number in the range $[l, r]$ should appear respectively.

Then a single line follows, containing $n$ integers describing the array $a$ ( $1 \leq a_i \leq 10^9$ ).

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

For each test case output $2$ numbers, $l$ and $r$ that satisfy the conditions, or "-1" if no numbers satisfy the conditions.

If multiple answers exist, you can output any.