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 <cstdio>
#include <algorithm>
#include <cstring>
#include <set>

#define maxn 200010
int a[maxn], b[maxn];
std::set<int> s;
int main()
{
	int n, k; scanf("%d%d", &n, &k);
	for (int i = 1; i <= n; ++i) scanf("%d", a + i);
	for (int i = 2; i <= n; ++i)
		b[i] = b[i - 1] + (a[i] > a[i - 1]);
	bool st = 0;
	for (int i = 1; i <= k; ++i)
		s.insert(a[i]);
	int ans = 1;
	if (b[k] == k - 1) st = 1;
	for (int i = k + 1; i <= n; ++i)
	{
		bool sorted = b[i] - b[i - k + 1] == k - 1;
//		printf("%d\n", sorted);
		{
			s.insert(a[i]);
			if (!(a[i - k] == *s.begin() && a[i] == *s.rbegin()))
			{
				if (!sorted || !st)
				{
					++ans;
					st |= sorted;
				}
			}
			s.erase(a[i - k]);
		}
	}
	printf("%d\n", ans );
	return 0;
}