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;
  vector<int> a(n);
  for(int i=0;i<n;i++){
    cin >> a[i];
  }
  vector<bool> b(n);
  int cnt=1;
  bool e=false;
  for(int i=1;i<n;i++){
    if(a[i]>a[i-1]){
      cnt++;
      if(cnt>=k){
        b[i]=true;
        e=true;
      }
    }
    else{
      cnt=1;
    }
  }
  set<int> st;
  int ans=0;
  bool f=false;
  for(int i=0;i<n;i++){
    if(i&&i<k){
      if(a[i-1]>a[i]){
        f=true;
      }
    }
    if(i>=k){
      auto itr=st.begin();
      auto itr2=st.end();
      itr2--;
      int u=*itr,v=*itr2;
      if(!(u==a[i-k]&&v<a[i])&&!b[i]){
        ans++;
      }
      st.erase(a[i-k]);
    }
    st.insert(a[i]);
  }
  if(e){
    ans++;
  }
  if(f){
    ans++;
  }
  cout << ans << endl;
}