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 A[200000];
set<int> S;

int main() {
    int n, k;
    cin >> n >> k;
    for (int i = 0; i < n; i++)
        cin >> A[i];

    int cnt = 0;
    int goodlen = 0;
    int ans = n - k + 1;
    for (int i = 0; i < n; i++) {
        if (i == 0 || A[i - 1] < A[i])
            goodlen++;
        else
            goodlen = 1;
        if (goodlen == k)
            cnt++;
        if (i >= k) {
            if (A[i] > *(S.rbegin()) && A[i - k] == *(S.begin()))
                ans--;
            S.erase(A[i - k]);
        }
        S.insert(A[i]);
    }
    if (cnt >= 2)
        ans -= cnt - 1;
    cout << ans << "\n";
}