F. Longest Strike
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$l = 13$$$, $$$r = 14$$$.

Input

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 $$$2 \cdot 10^5$$$.

Output

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.

Example
Input
4
7 2
11 11 12 13 13 14 14
5 1
6 3 5 2 1
6 4
4 3 4 3 3 4
14 2
1 1 2 2 2 3 3 3 3 4 4 4 4 4
Output
13 14
1 3
-1
1 4