Moamen and k-subarrays

Description:

Input:

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 $$$3\cdot10^5$$$.

Output:

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).

Sample Input:

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

Sample Output:

Yes
No
Yes

Note:

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.