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;
    vector <int> v(n);
    for (auto &x: v) cin >> x;
    int ans = 1;
    set <int> s;
    int leftSortedLength[n];
    leftSortedLength[0] = 1;
    for (int i = 1; i < n; i++) {
        leftSortedLength[i] = v[i] > v[i - 1] ? leftSortedLength[i - 1] + 1 : 1;
    }
    for (int i = 0; i < k; i++) s.insert(v[i]);
    bool found = leftSortedLength[k - 1] == k;
    for (int i = k; i < n; i++) {
        s.insert(v[i]);
        int mn = *s.begin(), mx = *s.rbegin();
        s.erase(v[i - k]);
        if (v[i - k] == mn && v[i] == mx) continue;
        if (leftSortedLength[i] != k)
            ans++;
        else if (!found)
            ans++, found = true;
    }
    cout << ans << "\n";
    return 0;
}