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 last last2

using namespace std;

int q1[200005],q2[200005];
int num[200005];

int main() {
  int n,k;
  scanf("%d%d",&n,&k);
  for(int i=1;i<=n;i++) scanf("%d",&num[i]);
  bool v=0;
  int ans=0,last=1;
  int l1=1,l2=1,r1=0,r2=0;
  for(int i=1;i<k;i++) {
  	  while (l1<=r1&&i-q1[l1]>k) l1++;
  	  while (l2<=r2&&i-q2[l2]>k) l2++;
  	  while (l1<=r1&&num[i]<num[q1[r1]]) r1--;
  	  q1[++r1]=i;
  	  while (l2<=r2&&num[i]>num[q2[r2]]) r2--;
  	  q2[++r2]=i;
	  if (num[i]<num[i-1]) last=i;
    }
  for(int i=k;i<=n;i++) {
  	while (l1<=r1&&i-q1[l1]>k) l1++;
  	while (l2<=r2&&i-q2[l2]>k) l2++;
  	while (l1<=r1&&num[i]<num[q1[r1]]) r1--;
  	q1[++r1]=i;
  	while (l2<=r2&&num[i]>num[q2[r2]]) r2--;
  	q2[++r2]=i;
  	if (num[i]<num[i-1]) last=i;
  	if (q1[l1]!=i-k||q2[l2]!=i) {
  		if (last<=i-k+1) {
  			if (!v) v=1,ans++;
		  }
  		else ans++;
	  }
  }
  printf("%d\n",ans);
  return 0;
}