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() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n, k;
    cin >> n >> k;
    vector<int> ps(n);
    for (int& p : ps) {
        cin >> p;
    }
    set<int> current_numbers(ps.begin(), ps.begin()+k);
    int count = 1;
    for (int i = k; i < n; ++i) {
        current_numbers.insert(ps[i]);
        int lo = *current_numbers.begin(), hi = *current_numbers.rbegin();
        count += lo != ps[i-k] || hi != ps[i];
        current_numbers.erase(ps[i-k]);
    }
    int sorted_stretches = 0;
    int current_stretch = 1;
    for (int i = 1; i < n; ++i) {
        if (ps[i] > ps[i-1]) {
            ++current_stretch;
        } else {
            current_stretch = 1;
        }
        sorted_stretches += current_stretch == k;
    }
    cout << count - max(sorted_stretches-1, 0) << endl;
    return 0;
}