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;
typedef long long ll;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
ll ans = 0;

int main()
{
ll n , k ;
cin >> n >> k ;
vector<ll> p(n);
rep(i, n){
  cin >> p[i];
}
vector<ll> pp(n);
ll a=0;
ll rr=0;
rep(i,n-1){
  if(p[i]<p[i+1])a++;
  else a=0;
  if(a>=k-1){
    pp[i-k+2]=1;
    rr++;
  }
}
set<ll> s;
rep(i,k){
  s.insert(p[i]);
}
rep(i,n-k){
  if(pp[i]==0){auto itrmi=s.begin();
  auto itrmx=s.end();itrmx--;
  if(*itrmi==p[i] && *itrmx<p[i+k])ans++;}
  s.erase(p[i]);
  s.insert(p[i+k]);
}
ll an=n-k+1-ans;
if(rr!=0){
  an-=rr-1;
}
cout << an << endl;
return 0;
}