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Chef's brother Chefu is a competitive programmer. Every day, he practices for ICPC (International Chefs' Programming Contest) by solving problems. Today, Chef challenged his brother to solve a certain problem, promising to bake an apple pie for him if he succeeds. Chefu has successfully solved the problem, but can you solve it?

You are given an integer sequence $A_{1}, A_{2}, \ldots, A_{N}$. In one move, you must select two adjacent elements of this sequence (i.e. $A_{i}$ and $A_{i+1}$ for some valid $i$) and swap them. Let's call a sequence orderly if it contains a contiguous subsequence with length at least $K$ such that all of its elements have identical values. Find the minimum number of moves required to make the given sequence orderly or determine that it is impossible.

------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains two space-separated integers $N$ and $K$.
The second line contains $N$ space-separated integers $A_{1}, A_{2}, \ldots, A_{N}$.

------ Output ------
For each test case, print a single line containing one integer — the minimum required number of moves, or $-1$ if it is impossible to make the sequence orderly.

------ Constraints ------
$1 ≤ T ≤ 1,000$
$2 ≤ K ≤ N ≤ 300,000$
$1 ≤ A_{i} ≤ 300,000$ for each valid $i$
the sum of $N$ over all test cases does not exceed $10^{6}$

------ Subtasks ------
Subtask #1 (30 points):
$N ≤ 100$
the sum of $N$ over all test cases does not exceed $1,000$

Subtask #2 (70 points): original constraints

----- Sample Input 1 ------
2
8 3
1 2 2 1 3 3 2 1
5 3
1 1 2 2 3
----- Sample Output 1 ------
3
-1

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