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<vector>
#include<set>
#include<queue>
using namespace std;
typedef long long ll;

int main(){
    int n, k;
    cin >> n >> k;
    vector<int> p(n), rev(n), sorted(n, 0);
    for(int i = 0; i < n; i++)  cin >> p[i], rev[p[i]] = i;
    for(int i = 1; i < n; i++){
        if(p[i-1] < p[i])   sorted[i] = 1;
        sorted[i] += sorted[i-1];
    }
    set<int> s;
    for(int i = 0; i < k; i++){
        s.insert(p[i]);
    }
    int ans = 0, flat = 0;
    if(sorted[k-1] == k-1)  flat++;
    else                    ans++;
    for(int i = 1; i <= n-k; i++){
        bool flag = (p[i-1] != *s.begin());
        s.erase(p[i-1]);
        s.insert(p[i+k-1]);
        flag |= (p[i+k-1] != *s.rbegin());
        if(sorted[i+k-1]-sorted[i] == k-1)  flat = 1;
        else if(flag)                       ans++;
    }
    cout << ans+flat << endl;
    return 0;
}