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 <iostream>
#include <set>
using namespace std;
typedef long long ll;
typedef pair<int, int> P;

int main(){
  int n, k; cin >> n >> k;
  if (n==k) return puts("1") * 0e1;
  int p[n]; for(int i=0; i<n; i++) cin >> p[i];
  int an = 1;
  set<int> s;
  for(int i=0; i<k; i++) {
    s.insert(p[i]);
  }
  for(int i=0; i<n-k; i++) {
    s.insert(p[i+k]);
    auto b=s.begin(), e=s.end(); e--;
    //cout << *b << " " << *e << " " << p[i] << " " << p[i+k] << endl;
    if (!(*b == p[i] && *e == p[i+k])) an++;
    s.erase(p[i]);
  }
  
  bool nt = false; int bf=-1, ct=0;
  for(int i=0; i<n; i++) {
    if (bf<p[i]) ct++; else ct=1; bf=p[i];
    if (ct==k) {nt=1;an--;}
  }
  
  cout << an+nt << endl;
}