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() {
  long n,k,a=0,ans;
  bool ss=false;
  cin >> n >> k;
  ans=n-k+1;
  vector<long> p(n);
  vector<bool> s(n-k+1,true);
  set<long> aaa;
  for(long i=0;i<n;i++) cin >> p[i];
  for(long i=0;i<n-1;i++) {
    if(p[i]<p[i+1]) a++;
    else a=0;
    if(a>=k-1) {
      s[i-k+2]=false;
      if(ss) ans--;
      else ss=true;
    }
  }
  for(long i=1;i<n-1;i++) {
    aaa.insert(p[i]);
    if(aaa.size()==k-1) {
      if(s[i-k+1]||s[i-k+2]){
        auto itr=aaa.begin();
        auto itr2=aaa.end();
        itr2--;
        if(p[i-k+1]<*itr&&p[i+1]>*itr2) ans--;
      }
      aaa.erase(aaa.lower_bound(p[i-k+2]));
    }
  }
  cout << ans << endl;
}