B. Quick Sorttime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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).InputThe 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.OutputFor 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.ExampleInput
43 21 2 33 13 1 24 21 3 2 44 22 3 1 4Output
0
1
1
2
NoteIn the first test case, the permutation is already sorted.In the second test case, you can choose element 3, and the permutation will become sorted as follows: [\color{red}{3}, 1, 2] \rightarrow [1, 2, \color{red}{3}].In the third test case, you can choose elements 3 and 4, and the permutation will become sorted as follows: [1, \color{red}{3}, 2, \color{red}{4}] \rightarrow [1, 2, \color{red}{3},\color{red}{4}].In the fourth test case, it can be shown that it is impossible to sort the permutation in 1 operation. However, if you choose elements 2 and 1 in the first operation, and choose elements 3 and 4 in the second operation, the permutation will become sorted as follows: [\color{red}{2}, 3, \color{red}{1}, 4] \rightarrow [\color{blue}{3}, \color{blue}{4}, \color{red}{1}, \color{red}{2}] \rightarrow [1,2, \color{blue}{3}, \color{blue}{4}].
43 21 2 33 13 1 24 21 3 2 44 22 3 1 4
0 1 1 2 
['greedy', 'math', '*900']