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;

int main(){
	int n,k;
	cin >> n >> k;
	int ans = n-k+1 , last = n , cont = 0;
	bool t = false;
	vector<int> x(n);
	set<int> s;
	for(int i = 0 ; i < n ; i += 1){
		cin >> x[i];
		if(x[i] > last){
			cont += 1;
		}else{
			cont = 1;
		}
		last = x[i];
		if(i >= k){
			s.erase(x[i-k]);
		}
		if(cont >= k){
			t = true;
			ans -= 1;
		}else if(i >= k){
			if(x[i-k] < *s.begin() && x[i] > *s.rbegin()){
				ans -= 1;
			}
		}
		s.insert(x[i]);
	}
	ans += t;
	cout << ans << endl;
}