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;
    set<int>s;
    vector<int>v(n);
    for(int i=0;i<n;i++)
        cin>>v[i];
    int cnt=1;
    for(int i=0;i<k;i++){
            s.insert(v[i]);
    }
    int l=0;
    for(int i=k;i<n;i++){
        s.erase(v[l]);
        l++;
        if(v[i]<*(s.rbegin())||v[l-1]>*(s.begin())){
            cnt++;
        }
        s.insert(v[i]);
    }
    int cntrp=0;
    int b=0,e=0;
    int f=0;
    for(int i=0;i<n;i++){
        while(v[b]>v[e]||e-b+1>k||(e-b+1>1&&v[e]<v[e-1])){
            b++;
        }
        if(e-b+1==k&&!f){
            cntrp++;
            f=1;
        }
        else if(e-b+1!=k){
            f=0;
        }
        e++;
    }
    if(cntrp)
        cnt-=(cntrp-1);
    cout << cnt << endl;
    return 0;
}
/**
5 3
0 2 1 4 3
4 4
0 1 2 3

10 4
2 0 1 3 7 5 4 6 8 9
*/