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;
#ifdef ONLINE_JUDGE
#define trace(...)
#endif

using LL = long long;

int a[200010];

int main() {
	ios_base::sync_with_stdio(false); cin.tie(NULL);
	int n, k; cin >> n >> k;
	int ans = n - k + 1;
	int prev = n, len = 0;
	int inc = 0;
	set<int> vals;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
		if (a[i] > prev) len++;
		else len = 1;
		prev = a[i];
		if (i >= k) vals.erase(a[i - k]);
		if (len >= k) { inc = 1; ans--; }
		else if (i >= k) {
			if (a[i - k] < *vals.begin() && a[i] > *vals.rbegin()) ans--;
		}
		vals.insert(a[i]);
	}
	ans += inc;
	cout << ans << endl;
	return 0;
}