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>
#define Maxn 200000
int a[Maxn+5];
int n,k;
int q_mx[Maxn+5],q_mn[Maxn+5];
int f_mx,t_mx,f_mn,t_mn;
int maxn[Maxn+5],minn[Maxn+5];
void push(int x){
	while(f_mx<=t_mx&&a[q_mx[t_mx]]<a[x]){
		t_mx--;
	}
	q_mx[++t_mx]=x;
	while(f_mn<=t_mn&&a[q_mn[t_mn]]>a[x]){
		t_mn--;
	}
	q_mn[++t_mn]=x;
}
void pop(int x){
	while(f_mx<=t_mx&&x-q_mx[f_mx]+1>k){
		f_mx++;
	}
	while(f_mn<=t_mn&&x-q_mn[f_mn]+1>k){
		f_mn++;
	}
}
int main(){
	scanf("%d%d",&n,&k);
	for(int i=1;i<=n;i++){
		scanf("%d",&a[i]);
	}
	f_mx=f_mn=1;
	t_mx=t_mn=0;
	for(int i=1;i<k;i++){
		push(i);
	}
	int ans=0;
	bool first=1;
	for(int i=k;i<=n;i++){
		push(i);
		pop(i);
		maxn[i]=a[q_mx[f_mx]];
		minn[i]=a[q_mn[f_mn]];
		if(maxn[i]==a[i]&&minn[i-1]<minn[i]){
			continue;
		}
		if(t_mn-f_mn+1==k){
			if(first){
				ans++;
				first=0;
			}
			continue;
		}
		ans++;
	}
	printf("%d\n",ans);
	return 0;
}