Problem: Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).

Now, he will perform the following operation exactly once:

* Choose K consecutive elements in P and sort them in ascending order.



Find the number of permutations that can be produced as P after the operation.

Constraints

* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
P_0 P_1 \cdots P_{N-1}


Output

Print the number of permutations that can be produced as P after the operation.

Examples

Input

5 3
0 2 1 4 3


Output

2


Input

4 4
0 1 2 3


Output

1


Input

10 4
2 0 1 3 7 5 4 6 8 9


Output

6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int main() {
  int n, k;
  cin>>n>>k;
  int p[n];
  for (int i=0; i<n; i++) cin>>p[i];

  int i = 0;
  int ans = 0;
  set<int> nums;
  for (int i=0; i<k-1; i++) {
    nums.insert(p[i]);
  }
  while (i + k - 1 < n) {
    ++ans;
    nums.insert(p[i+k-1]);
    nums.erase(p[i]);
    while (i + k < n) {
      int min_nums = *nums.begin();
      auto it = nums.end();
      int max_nums = *(--it);
      if (!(p[i] < min_nums && max_nums < p[i+k])) {
        break;
      }
      ++i;
      if (i + k - 1 == n) {
        break;
      }
      nums.insert(p[i+k-1]);
      nums.erase(p[i]);
    }
    ++i;
  }
  int cnt_inc_seq = 0;
  i = 1;
  while (i < n) {
    int len = 0;
    while (i < n && p[i-1] < p[i]) {
      ++len;
      ++i;
    }
    if (len >= k - 1) {
      ++cnt_inc_seq;
    }
    ++i;
  }
  if (cnt_inc_seq > 1) {
    ans -= cnt_inc_seq - 1;
  }
  cout<<ans<<endl;
}