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;
int n,k;
const int maxn=200005;
int a[maxn];
int ans;
set<int> st;
int b[maxn];
int main()
{
    scanf("%d%d",&n,&k);
    for(int i=1;i<=n;i++)
        scanf("%d",&a[i]);
    int now=1;
    int cnt=0;
    for(int i=2;i<=n;i++)
    {
        if(a[i]<a[i-1])now=i;
        if(i-now+1>=k)b[i]=1,cnt=1;
    }
    if(!b[k])ans=1;
    for(int i=1;i<=k;i++)
    {
        st.insert(a[i]);
    }
    for(int i=k+1;i<=n;i++)
    {
        ans++;
        if(b[i]||(st.lower_bound(a[i])==st.end()&&st.lower_bound(a[i-k])==st.begin()))
        {
            ans--;
        }
        st.erase(a[i-k]);
        st.insert(a[i]);
    }
    cout<<ans+cnt<<endl;
}