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;

#define ll long long


int main(){
  int n, k;
  cin >> n >> k;
  
  vector<int> p(n);
  for(int i = 0; i < n; i++) cin >> p[i];
  priority_queue<int> q0, q1;
  vector<int> fin(n, false);
  vector<int> seq(n, 1);
  for(int i = 0; i < k; i++){
    q0.push(p[i]);
    q1.push(-p[i]);
  }
  for(int i = n - 2; i >= 0; i--){
    if(p[i] < p[i + 1]) seq[i] = seq[i + 1] + 1;
  }
  ll s = 0;
  for(int i = 0; i < n; i++){
    if(seq[i] == k) s++;
  }
  ll count = 1;
  for(int i = 0; i + k < n; i++){
    while(fin[-q1.top()]){
      q1.pop();
    }
    ll c = 0;
    if(-q1.top() != p[i]) c = 1;
    fin[p[i]] = true;
    while(fin[q0.top()]){
      q0.pop();
    }
    q0.push(p[i + k]);
    q1.push(-p[i + k]);
    if(q0.top() != p[i + k]) c = 1;
    count += c;
  }
  
  cout << (count - max(s - (ll)1, (ll)0)) << endl;
  
  return 0;
}