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>
#define SIZE 200005
using namespace std;

int A[SIZE];
bool id[SIZE];

int main()
{
	int n,k;
	scanf("%d %d",&n,&k);
	for(int i=0;i<n;i++) scanf("%d",&A[i]);
	int cnt=0;
	for(int i=1;i<k;i++) cnt+=(A[i]>A[i-1]);
	for(int i=0;i+k<=n;i++)
	{
		id[i]=(cnt==k-1);
		if(i==n-k) break;
		cnt-=(A[i+1]>A[i]);
		cnt+=(A[i+k]>A[i+k-1]);
	}
	set <int> st;
	set <int>::iterator it;
	for(int i=0;i<k;i++) st.insert(A[i]);
	int ret=(id[0]?0:1);
	for(int i=1;i+k<=n;i++)
	{
		bool up=false;
		st.insert(A[i+k-1]);
		it=st.end();it--;
		up|=!(*it==A[i+k-1]);
		it=st.begin();
		up|=!(*it==A[i-1]);
		up&=!id[i];
		ret+=up;
		st.erase(A[i-1]);
	}
	for(int i=0;i<n;i++)
	{
		if(id[i])
		{
			ret++;
			break;
		}
	}
	printf("%d\n",ret);
}