A14376 | Moamen and k-subarrays

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).