A15650 | Quick Sort

You are given a permutation $^\dagger$ $p$ of length $n$ and a positive integer $k \le n$ .

In one operation, you:

- Choose $k$ distinct elements $p_{i_1}, p_{i_2}, \ldots, p_{i_k}$ .
- Remove them and then add them sorted in increasing order to the end of the permutation.

For example, if $p = [2,5,1,3,4]$ and $k = 2$ and you choose $5$ and $3$ as the elements for the operation, then $[2, \color{red}{5}, 1, \color{red}{3}, 4] \rightarrow [2, 1, 4, \color{red}{3},\color{red}{5}]$ .

Find the minimum number of operations needed to sort the permutation in increasing order. It can be proven that it is always possible to do so.

$^\dagger$ A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ( $2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ( $n=3$ but there is $4$ in the array).

The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. The description of test cases follows.

The first line of each test case contains two integers $n$ and $k$ ( $2 \le n \le 10^5$ , $1 \le k \le n$ ).

The second line of each test case contains $n$ integers $p_1,p_2,\ldots, p_n$ ( $1 \le p_i \le n$ ). It is guaranteed that $p$ is a permutation.

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

For each test case output a single integer — the minimum number of operations needed to sort the permutation. It can be proven that it is always possible to do so.