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:
  
    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?
  
  Input
  
  The first line contains a single integer t (1 ≤ t ≤ 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 ≤ k ≤ n ≤ 10^5).
  
  The second line contains n integers a_1, a_2, …, a_n (0 ≤ |a_i| ≤ 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⋅10^5.
  
  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).
  
  Example
  
  Input
  
  
  3
  5 4
  6 3 4 2 1
  4 2
  1 -4 0 -2
  5 1
  1 2 3 4 5
  
  
  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.
solution: #include <bits/stdc++.h>
  using namespace std;
  ostream& operator<<(ostream& os, pair<int, int> a) {
    return os << a.first << " " << a.second;
  }
  int x4[] = {0, 1, 0, -1};
  int y4[] = {1, 0, -1, 0};
  int binary_search(int x, vector<int>& ara) {
    int low = 0;
    int high = ara.size() - 1;
    int mid;
    while (low <= high) {
      mid = (low + high) / 2;
      if (ara[mid] == x) {
        return mid;
      } else if (ara[mid] > x) {
        high = mid - 1;
      } else {
        low = mid + 1;
      }
    }
    return -1;
  }
  int main() {
    ios_base::sync_with_stdio(false), cin.tie(nullptr);
    int t;
    cin >> t;
    int n, k;
    while (t--) {
      cin >> n >> k;
      vector<int> ara(n), pos(n);
      for (auto& i : (ara)) {
        cin >> i;
      }
      pos = ara;
      sort(pos.begin(), pos.end());
      for (int i = 0; i < n; ++i) {
        int x = binary_search(ara[i], pos);
        if (x == n - 1) {
          k--;
        } else if (i + 1 < n and x + 1 < n and ara[i + 1] != pos[x + 1]) {
          k--;
        } else if (i == n - 1) {
          k--;
        }
      }
      k >= 0 ? cout << "YES"
                    << "\n"
             : cout << "NO"
                    << "\n";
    }
    return 0;
  }
  