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 maxn 200050
using namespace std;

int n,m;
int a[maxn];

set<int> s;

bool ok[maxn];

int l[maxn];
int L[maxn],R[maxn];

int main()  {
    scanf("%d%d",&n,&m);
    for (int i=1;i<=n;++i)
        scanf("%d",a+i);

    for (int i=1;i<=n;++i)  {
        s.insert(a[i]);
        if (i<m)   continue;
        L[i]=*s.begin();
        R[i]=*s.rbegin();
        s.erase(a[i-m+1]);
        // cout<<i<<":"<<L[i]<<" "<<R[i]<<endl;
    }
    int ans=ok[m]=1;
    for (int i=m+1;i<=n;++i)    
        if (!(a[i-m]<L[i]&&a[i]>R[i-1]))
            ++ans,ok[i]=1;
    for (int i=1,j=1;i<=n;i=j+1)  {
        for (j=i;j<=n&&a[j]<=a[j+1];)    ++j;
        for (int k=i;k<=j;++k)
            l[k]=i;
    }
    bool flag=0;
    for (int i=1;i<=n;++i)
        if (ok[i]&&i-l[i]+1>=m)
            --ans,flag=1;
    ans+=flag;
    printf("%d\n",ans);
    return 0;
}