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;
 

// 解説を読んで
// Pの文字列を線形探索していく
// まったくソートできてない場合は「n - k + 1」となり
// 昇順にソートしている場合は上記数値をカウントダウンする。

int main(){
	int n,k;
	cin >> n >> k;

    vector<int> P(n);
    set<int> S;
    int count;
    int last;
    int answer = n - k + 1;
    bool sorted = false;

    for (int i = 0; i < n; i++) {
        cin >> P[i];

        if (P[i] > last) {
            count++;
        } else {
            count = 1;
        }
        last = P[i];

        if (i >= k) {
            S.erase(P[i - k]);
        }

        if (count >= k) {
            sorted = true;
            answer--;
        } else if (i >= k
        && P[i - k] < *S.begin() 
        && P[i] > *S.rbegin()) {
            answer--;
        }
        S.insert(P[i]);
    }
    if (sorted) answer++;
    cout << answer << endl;
}