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, c, cnt, ans=1, a[200005];
set<int> st;
int main() {
	int i;
	cin >> n >> k;
	for(i=0; i<n; i++) scanf("%d", &a[i]);
	for(i=0; i<n-1; i++) {
		if(a[i] < a[i+1]) c++;
		else c = 0;
		if(c == k-1) cnt++;
	}
	for(i=0; i<k; i++) st.insert(a[i]);
	for(; i<n; i++) {
		st.erase(a[i-k]);
		if(a[i-k] > *st.begin() || a[i] < *st.rbegin()) ans++;
		st.insert(a[i]);
	}
	cout << ans - max(0, cnt-1);
	return 0;
}