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 rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep_in(i, s, n) for (int i = (s); i < (int)(n); i++)
typedef int64_t ll;

int main() {
  int n,k;
  cin>>n>>k;

  vector<int> p(n);
  rep(i,n){
    cin>>p[i];
  }

  set<int> s;
  rep(i,k){
    s.insert(p[i]);
  }
  int out=1;
  rep(i,n-k){
    s.insert(p[i+k]);
    if(*s.begin()!=p[i]||*s.rbegin()!=p[i+k]) out++;
    s.erase(p[i]);
  }

  int sorted_seq=0;
  int len=0;
  rep(i,n-1){
    if(p[i]>p[i+1]) len=0;
    len++;
    if(len==k){
      sorted_seq++;
    }
  }
  out-=(sorted_seq-(sorted_seq>0));

  cout<<out<<endl;
}