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(){
    int N, K; cin >> N >> K;
    vector<int> a(N);
    for(auto& t : a) cin >> t;
    set<int> S;
    int prev = 100;
    int cnt = 0;
    int sr = 0;
    int res = 0;
    for(int i=0;i<N;i++){
        if(prev > a[i]) cnt = 1;
        else ++cnt;
        prev = a[i];
        if(cnt >= K) sr = 1;
        else if(i >= K-1) ++res;
        S.insert(a[i]);
        if(i >= K){
            if(cnt < K && *S.rbegin() == a[i] && *S.begin() == a[i-K]) --res;
            S.erase(a[i-K]);
        }
    }
    cout << res + sr << endl;
}