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 <iostream>
#include <cstdio>
#include <set>

using namespace std;

int n, k;
int ans, now;
bool v, v2;
int a[200005];
set<int> se;

int main()
{
    //freopen("input.txt", "r", stdin);
    scanf("%d%d", &n, &k);
    for(int i = 0; i < n; i++) scanf("%d", &a[i]);
    ans = n - k + 1;
    for(int i = 0; i < k - 1; i++) if(a[i] < a[i + 1]) now++;
    for(int i = k - 1; i <= n - 1; i++)
    {
        if(now == k - 1 && !v) ans--, v2 = true, v = true;
        else if(now == k - 1) v = true;
        else v = false;
        if(a[i] < a[i + 1]) now++;
        if(a[i - k + 1] < a[i - k + 2]) now--;
    }
    if(v2) ans++;
    for(int i = 0; i < k; i++) se.insert(a[i]);
    for(int i = k; i < n; i++)
    {
        se.insert(a[i]);
        if(*se.begin() == a[i - k] && *se.rbegin() == a[i]) ans--;
        se.erase(a[i - k]);
    }
    printf("%d", ans);
    return 0;
}