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;

const int maxn = 2e5 + 5;

int n, a[maxn], k;
vector<int> fucks;

bool isSorted(int l, int r) {
	r--;
	return upper_bound(fucks.begin(), fucks.end(), r) == lower_bound(fucks.begin(), fucks.end(), l);
}

int main(int argc, char const *argv[])
{
	// freopen("in", "r", stdin);
	cin >> n >> k;
	for(int i = 1; i <= n; i++) {
		cin >> a[i];
		if(i != 1) {
			if(a[i-1] > a[i]) {
				fucks.emplace_back(i-1);
			}
		}
	}
	int took_identical = 0, ans = 1;
	if(isSorted(1, k)) took_identical = 1;

	set<int> st;
	for(int i = 2; i <= k; i++) {
		st.insert(a[i]);
	}
	for(int l = 1, r = k + 1; r <= n; l++, r++) {
		if(a[l] < *st.begin() and *st.rbegin() < a[r]) {}
		else {
			if(isSorted(l + 1, r)) {
				if(!took_identical) {
					took_identical = 1;
					ans++;
				}
			} else {
				ans++;
			}
		}
		st.erase(a[l + 1]);
		st.insert(a[r]);
	}
	cout << ans << endl;
	return 0;
}