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;
  vector<int> p(n);
  for (int i = 0; i < n; i++) cin >> p.at(i);
  int ans = 1, increase = 0, nochange = 0;
  for (int i = 0; i < n - 1; i++) {
    if (p.at(i) > p.at(i + 1)) {
      increase = 0;
    } else {
      increase++;
      if (increase == k - 1) nochange++;
    }
  }
  set<int> s;
  for (int i = 0; i < k; i++) s.insert(p.at(i));
  for (int i = k; i < n; i++) {
    int prevmin = *s.begin(), prevmax = *s.rbegin();
    s.erase(p.at(i - k));
    s.insert(p.at(i));
    if (prevmin == p.at(i - k) && prevmax <= p.at(i)) continue;
    ans++;
  }
  cout << ans - max(0, nochange - 1) << endl;
}