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<cstdio>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<deque>
#define ll long long
using namespace std;
deque<ll>qmax,qmin;

ll n,k,p,t,a[200007],f[200007];

int main(){
    scanf("%lld%lld",&n,&k);
    for (int i=1;i<=n;++i){
        scanf("%lld",&a[i]);
        f[i]=1;
        if (a[i]>a[i-1]) f[i]+=f[i-1];
        if (!qmax.empty()&&qmax.front()<=i-k) qmax.pop_front();
        if (!qmin.empty()&&qmin.front()<=i-k) qmin.pop_front();
        while (!qmax.empty()&&a[qmax.back()]<a[i]) qmax.pop_back();
        while (!qmin.empty()&&a[qmin.back()]>a[i]) qmin.pop_back();
        qmax.push_back(i),qmin.push_back(i);
        if (i>=k&&f[i]<k){
            ++p;
            if (i-1>=k&&f[i-1]<k&&qmax.size()==1&&a[i-k]<a[qmin.front()])
                --p;
        }
        t=max(t,f[i]);
    }
    if (t>=k) ++p;
    printf("%lld",p);
}