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>

using namespace std;
const int maxn=200000+200;
int a[maxn];
int r[maxn];
int n,k;
set<int> s;
typedef set<int>::iterator it;
int c1,c2,c3;
it m1,m2,m3;
int sta[maxn];
int e=0;
int main()
{
    cin>>n>>k;
    for(int i=1;i<=n;i++){
        cin>>a[i];
    }
    for(int i=1;i<=k;i++){
        s.insert(a[i]);
    }
    for(int i=1;i<=n;i++){
        while(e!=0&&a[sta[e-1]]>a[i])e--;
        sta[e++]=i;
        r[i]=e;
    }
    c3=1;
    if((r[k]-r[1])==k-1){
        c2+=1;
        c3=0;
    }
    for(int i=2;i<=(n-k+1);i++){
        m1=s.begin();
        m2=s.end();
        m2--;
        if(a[i-1]==(*m1)&&a[i+k-1]>(*m2))
            c1+=1;
        else if((r[i+k-1]-r[i])==k-1)
            c2+=1;
        else
            c3+=1;
        s.erase(s.lower_bound(a[i-1]));
        s.insert(a[i+k-1]);
    }
    if(c2>1)c2=1;
    c3+=c2;
    cout<<c3<<endl;
    return 0;
}
/*
8 2
1 3 5 7 2 4 6 8


*/