codeforces#P1557B. Moamen and k-subarrays
Moamen and k-subarrays
Description
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?
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).
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).
Samples
3
5 4
6 3 4 2 1
4 2
1 -4 0 -2
5 1
1 2 3 4 5
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 $\{ [6], [3, 4], [2], [1] \}$.
- Reorder them: $\{ [1], [2], [3,4], [6] \}$.
- 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.