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 mem(s,t) memset(s,t,sizeof(s))
#define pb(s) push_back(s)
#define inf 0x3f3f3f3f
#define mn 100010
typedef long long ll;
using namespace std;
struct node{
	node(){}
	node(int i,int n):i(i),n(n){}
	int i,n;
	bool operator<(const node& t)const{return n<t.n;}
};
int P[200010];
int main()
{
	int n,k;scanf("%d%d",&n,&k);
	for(int i=0;i<n;++i)scanf("%d",P+i);
	int lis=1;
	priority_queue<node> qa,qi;
	for(int i=0;i<k;++i){
		if(i&&P[i]>P[i-1])++lis;
		else lis=1;
		qa.push(node(i,P[i]));
		qi.push(node(i,-P[i]));
	}
	int ans=1;
	bool ok=1;
	if(lis>=k)ok=0;
	for(int i=k;i<n;++i){
		while(!qa.empty()&&qa.top().i<=i-k)qa.pop();
		while(!qi.empty()&&qi.top().i<=i-k)qi.pop();
		if(P[i]>P[i-1])++lis;
		else lis=1;
		if(P[i-k]<-1*qi.top().n&&P[i]>qa.top().n);
		else if(lis>=k){
			if(ok)ok=0,++ans;
		}
		else ++ans;
		qa.push(node(i,P[i]));
		qi.push(node(i,-P[i]));
	}
	printf("%d\n",ans);
    return 0;
}