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 st first
#define nd second
#define ii pair<int,int>
#define orta ((bas+son)>>1)
#define pb push_back
#define N 200005
#define LOG 22
#define ll long long
#define MOD 998244353
using namespace std;

int n,k;
int a[N],sr[N];
bool flag;

bool ch(int l,int r) {

	bool res=sr[r]>l;

	flag|=(!res);

	return res;

}

int main() {

	scanf("%d %d",&n,&k);

	for(int i=1;i<=n;i++) {

		scanf("%d",a+i);

	}

	sr[1]=1;

	for(int i=2;i<=n;i++) {

		if(a[i]>=a[i-1]) sr[i]=sr[i-1];
		else sr[i]=i;

	}

	int ptr=0;
	int cnt=ch(1,k);

	multiset<int> s;

	for(int i=1;i<=n-k+1;i++) {

		while(ptr+1<=i+k-1) {

			++ptr;

			s.insert(a[ptr]);

		}

		if(!(i+k<=n) || (a[i]==*s.begin() && a[i+k]>*s.rbegin()));
		else cnt+=ch(i+1,i+k);

		s.erase(s.find(a[i]));

	}

	printf("%d",cnt+flag);

}