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 <vector>
#include <set>
using namespace std;
int main(void){
    int n, k, ans = 0;
    vector<int> p;
    set<int> s, u;
    cin >> n >> k;
    p.assign(n, 0);
    for(int i=0;i<n;i++){
        cin >> p[i];
    }

    int v = 0;
    for(int i=1;i<n;i++){
        if(p[i] < p[i-1]){
            v = i;
        }
        if(i-v+1 >= k){
            u.insert(i-k+1);
        }
    }

    for(int i=0;i<k;i++){
        s.insert(p[i]);
    }
    ans = n-k+1;
    for(int i=0;i<n-k;i++){
        s.erase(p[i]);
        auto mn = s.begin();
        auto mx = s.end(); mx--;

        if(p[i] < (*mn) && (*mx) < p[i+k]){
            if(u.find(i) == u.end() || u.find(i+1) == u.end())ans--;
        }

        s.insert(p[i+k]);

    }

    if(u.size() > 1){
        ans -= u.size()-1;
    }


    cout << ans << endl;

}