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;

set<int> S;
int n, k, a[210000];

int main() {
    scanf("%d%d", &n, &k);
    int ans = 1;
    for (int i = 1; i <= n; i++) {
        scanf("%d", &a[i]);
        if (i <= k) {
            S.insert(a[i]);
        } else {
            int Mi = *S.begin();
            S.erase(a[i - k]);
            S.insert(a[i]);
            int Ma = *S.rbegin();
            if (!(Mi == a[i - k] && Ma == a[i]))
                ans++;
        }
    }
    int now = 0, now2 = 0;
    for (int i = 1; i <= n; i++)
        if (a[i] >= a[i - 1]) {
            now++;
        } else {
            if (now >= k) now2++;
            now = 1;
        }
    if (now >= k) now2++;
    ans -= max(now2 - 1, 0);
    printf("%d\n", ans);
    return 0;
}