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 <algorithm>
#include <vector>
#include <set>
#define rep(i,n) for(int i=0;i<n;++i)
#define rep1(i,n) for(int i=1;i<=n;++i)
using namespace std;
int main()
{
  int n,k;cin >> n >> k;
  vector<int> p(n);
  rep(i,n) cin >> p[i];
  set<int> st;
  rep(i,k) st.insert(p[i]);
  int left = 0;
  int right = k;
  int res = 1;
  while(right < n) {
    bool f = true;
    auto lit = st.find(p[left]);
    if(lit != st.begin() ) f = false;
    st.erase(p[left]);
    st.insert(p[right]);
    auto rit = st.find(p[right]);
    rit++;
    if(rit != st.end()) f = false;
    if(!f) res++;
    left++;
    right++;
  }

  int cnt = 1;
  int kk = 0;
  rep(i,n-1) {
    if(p[i] < p[i+1]) cnt++;
    else {
      if(cnt >= k) kk++;
      cnt = 1;
    }
  }
  if(cnt >= k) kk++;
  res -= max(kk - 1, 0);
  cout << res << "\n";
  return 0;
}