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;

const int MAXN = 200005;

int n, k, p[MAXN], minP[MAXN], maxP[MAXN], dp[MAXN];

int main() {
    scanf("%d%d", &n, &k);
    for(int i = 0; i < n; ++i)
        scanf("%d", &p[i]);

    set<int> s;
    for(int i = 0; i < n; ++i) {
        s.insert(p[i]);
        if (i >= k-2) {
            minP[i-k+2] = *s.begin();
            maxP[i-k+2] = *s.rbegin();
            s.erase(p[i-k+2]);
        }
    }

    dp[n-1] = 1;
    for(int i = n-2; i >= 0; --i)
        dp[i] = (p[i] < p[i+1]) ? (dp[i+1] + 1) : 1;

    bool original = false;
    int ans = 0;

    for(int i = k-1; i < n; ++i) {
        if (dp[i-k+1] >= k)
            original = true;
        else if (i == k-1 || maxP[i-k+1] > p[i] || p[i-k] > minP[i-k+1])
            ++ans;
    }
    if (original)
        ++ans;

    printf("%d", ans);

    return 0;
}