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 rep(i,n) for(int i=0;i<n;i++)
using namespace std;
typedef long long ll;

ll n,k,p[200000],x[200000];
set<int> st;

int main(){
    cin>>n>>k;
    ll ans=n-k+1;
    rep(i,n)cin>>p[i];
    rep(i,k)st.insert(p[i]);
    rep(i,n-k){
        st.insert(p[i+k]);
        auto itr=st.end();
        itr--;
        if(*st.begin()==p[i]&&*itr==p[i+k])ans--;
        st.erase(p[i]);
    }
    int aaa=0;
    for(int i=1;i<n;i++){
        if(p[i-1]<p[i])x[i]=x[i-1]+1;
        if(x[i]==k-1)ans--,aaa=1;
    }
    cout<<ans+aaa<<endl;
}