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;
const int MOD=1e9+7;
//const int MOD=998244353;
const int INF=1e9;
const long long LINF=1e18;
#define int long long
//template
template <typename T>
void fin(T a){
  cout<<a<<endl;
  exit(0);
}
//main
signed main(){
  int N,K;cin>>N>>K;
  std::vector<int> v(N);
  for(int i=0;i<N;i++)cin>>v[i];
  set<int> s;
  for(int i=0;i<K;i++)s.insert(v[i]);
  int ans=1;
  for(int i=K;i<N;i++){
    bool f=false;
    if(v[i-K]!=*s.begin())f=true;
    if(v[i]<*s.rbegin())f=true;
    //cout<<i<<" "<<*s.begin()<<" "<<*s.rbegin()<<endl;
    ans+=f;
    s.erase(v[i-K]);
    s.insert(v[i]);
    //cout<<i<<" "<<ans<<endl;
  }
  int mn=INF,mx=-1;
  int cnt=0;
  int a=0;
  for(int i=0;i<N;i++){
    if(mx<v[i]){
      cnt++;
    }
    else cnt=1;
    mx=v[i];
    if(cnt>=K){
      a++;
      cnt=-INF;
    }
  }
  //cout<<ans<<endl;
  //cout<<a<<endl;
  ans-=max(0LL,a-1);
  fin(ans);
}