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;
using ll = long long;
using ull = unsigned long long;
using P = pair<int,int>;
#define rep(i,n) for(ll i = 0;i < (ll)n;i++)
#define ALL(x) (x).begin(),(x).end()
#define MOD 1000000007



int main(){
  
  int n,k;
  cin >> n >> k;
  vector<int> v(n);
  rep(i,n)cin >> v[i];
  set<int> st;
  rep(i,k)st.insert(v[i]);
  int res = 1;
  for(int i = k;i < n;i++){
    if(*st.begin() == v[i-k]){
      if(*st.rbegin() > v[i])res++;
    }else{
      res++;
    }
    st.erase(v[i-k]);
    st.insert(v[i]);
  }
  int cnt = 0,s = 0;
  rep(i,n){
    if(i == 0 || v[i-1] < v[i])cnt++;
    else {
      if(cnt >= k)s++;
      cnt = 1;
    }
  }
  if(cnt >= k)s++;
  cout << (s != 0 ? res-s+1 : res) << endl;





  return 0;
}