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;
  int bsg(int arr[], int n, int v) {
    int l = 0, r = n - 1, m;
    while (l <= r) {
      m = (l + r) / 2;
      if (arr[m] == v) return m;
      if (arr[m] > v) {
        if (m == l || arr[m - 1] < v) return m;
        r = m - 1;
      } else {
        l = m + 1;
      }
    }
    return n;
  }
  int bsl(int arr[], int n, int v) {
    int l = 0, r = n - 1, m;
    while (l <= r) {
      m = (l + r) / 2;
      if (arr[m] == v) return m;
      if (arr[m] < v) {
        if (m == r || arr[m + 1] > v) return m;
        l = m + 1;
      } else {
        r = m - 1;
      }
    }
    return -1;
  }
  int main() {
    int t;
    cin >> t;
    while (t--) {
      int n, i, j, k, p, q;
      cin >> n >> k;
      int arr[n], brr[n];
      for (i = 0; i < n; i++) {
        cin >> arr[i];
        brr[i] = arr[i];
      }
      sort(brr, brr + n);
      j = 1;
      for (i = 1; i < n; i++) {
        if (arr[i] < arr[i - 1])
          j++;
        else {
          p = bsg(brr, n, arr[i - 1] + 1);
          q = bsl(brr, n, arr[i] - 1);
          if (p <= q) j++;
        }
      }
      if (j <= k)
        cout << "Yes" << endl;
      else
        cout << "No\n";
    }
    return 0;
  }
  