[Solution] Moamen and k-subarrays solution codeforces

Moamen and k-subarrays solution codeforces

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:

Split the array into exactly k non-empty subarrays such that each element belongs to exactly one subarray.

Reorder these subarrays arbitrary.

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?

Moamen and k-subarrays solution codeforces

Input

The first line contains a single integer t (1≤t≤103) — the number of test cases. The description of the test cases follows.

Moamen and k-subarrays solution codeforces

The first line of each test case contains two integers n and k (1≤k≤n≤105).

Moamen and k-subarrays solution codeforces

The second line contains n integers a1,a2,…,an (0≤|ai|≤109). It is guaranteed that all numbers are distinct.

It is guaranteed that the sum of n over all test cases does not exceed 3⋅105.

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).

Example

inputCopy

3

5 4

6 3 4 2 1

4 2

1 -4 0 -2

5 1

1 2 3 4 5

outputCopy

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:

Split a into {,[3,4],,}.

Reorder them: {,,[3,4],}.

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.