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> a(n),mina(n-k+1),maxa(n-k+1);
  vector<int> dec(n,0),srt(n-k+1,0);
  vector<bool> chg(n-k+1,false);
  for(auto &i:a)cin>>i;
  deque<int> dq;
  for(int i=0;i<n;++i){
    while(!dq.empty()&&a[dq.back()]>=a[i])dq.pop_back();
    dq.push_back(i);
    if(dq.front()==i-k)dq.pop_front();
    if(i>=k-1)mina[i-k+1]=a[dq.front()];
  }
  dq.clear();
  for(int i=0;i<n;++i){
    while(!dq.empty()&&a[dq.back()]<=a[i])dq.pop_back();
    dq.push_back(i);
    if(dq.front()==i-k)dq.pop_front();
    if(i>=k-1)maxa[i-k+1]=a[dq.front()];
  }
  for(int i=1;i<n;++i)dec[i]+=dec[i-1]+(a[i-1]>a[i]);
  for(int i=0;i<n-k+1;++i)srt[i]=dec[i+k-1]-dec[i];
  for(int i=1;i<n-k+1;++i){
    if(a[i-1]!=mina[i-1]||a[i+k-1]!=maxa[i])chg[i]=true;
  }
  int r=0,d=0;
  for(int i=0;i<n-k+1;++i){
    if(srt[i]&&(!i||chg[i]))r++;
    else if(!srt[i])d=1;
  }
  cout<<r+d;
}