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 Z=N+1-K,A=-1;
  vector<int> p(N);
  for(int i=0;i<N;i++){
    cin>>p[i];
  }
  deque<int> MIN;
  deque<int> MAX;
  for(int i=0;i<N;i++){
    while(!MIN.empty()){
      if(p[MIN.back()]<p[i]){
        break;
      }
      MIN.pop_back();
    }
    MIN.push_back(i);
    while(!MAX.empty()){
      if(p[MAX.back()]>p[i]){
        break;
      }
      MAX.pop_back();
    }
    MAX.push_back(i);
    if(i>=K){
      if(MIN.size()==K+1){
        Z++;
      }
      if(MIN.front()==i-K&&MAX.front()==i){
        Z--;
      }
      if(MIN.front()==i-K){
        MIN.pop_front();
      }
      if(MAX.front()==i-K){
        MAX.pop_front();
      }
    }
    if(i>=K-1){
      if(MIN.size()==K){
        A++;
      }
    }
  }
  cout<<Z-max(0,A)<<endl;
}