B. Moamen and k-subarrays
time limit per test
2 seconds
memory limit per test
256 megabytes
standard input
standard output

Moamen has an array of $$$n$$$ distinct integers. He wants to sort that array in non-decreasing order by doing the following operations in order exactly once:

  1. Split the array into exactly $$$k$$$ non-empty subarrays such that each element belongs to exactly one subarray.
  2. Reorder these subarrays arbitrary.
  3. Merge the subarrays in their new order.

A sequence $$$a$$$ is a subarray of a sequence $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Can you tell Moamen if there is a way to sort the array in non-decreasing order using the operations written above?


The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^3$$$) — the number of test cases. The description of the test cases follows.

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

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le |a_i| \le 10^9$$$). It is guaranteed that all numbers are distinct.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$3\cdot10^5$$$.


For each test case, you should output a single string.

If Moamen can sort the array in non-decreasing order, output "YES" (without quotes). Otherwise, output "NO" (without quotes).

You can print each letter of "YES" and "NO" in any case (upper or lower).

5 4
6 3 4 2 1
4 2
1 -4 0 -2
5 1
1 2 3 4 5

In the first test case, $$$a = [6, 3, 4, 2, 1]$$$, and $$$k = 4$$$, so we can do the operations as follows:

  1. Split $$$a$$$ into $$$\{ [6], [3, 4], [2], [1] \}$$$.
  2. Reorder them: $$$\{ [1], [2], [3,4], [6] \}$$$.
  3. Merge them: $$$[1, 2, 3, 4, 6]$$$, so now the array is sorted.

In the second test case, there is no way to sort the array by splitting it into only $$$2$$$ subarrays.

As an example, if we split it into $$$\{ [1, -4], [0, -2] \}$$$, we can reorder them into $$$\{ [1, -4], [0, -2] \}$$$ or $$$\{ [0, -2], [1, -4] \}$$$. However, after merging the subarrays, it is impossible to get a sorted array.