Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

5 3
0 2 1 4 3

Sample Output 1

2

Two permutations can be produced as P after the operation: (0,1,2,4,3) and (0,2,1,3,4).

Sample Input 2

4 4
0 1 2 3

Sample Output 2

1

Sample Input 3

10 4
2 0 1 3 7 5 4 6 8 9

Sample Output 3

6

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i,n) for(int i=0; i<(n); i++)

using namespace std;

typedef long long ll;
typedef pair<int, int> P;
const int INF = 1000000;

#define N 200005
int a[N];
deque<int> q1,q2;
void push(int x)
{
    while(!q1.empty()&&a[q1.back()]>a[x]) q1.pop_back();
    q1.push_back(x);
    while(!q2.empty()&&a[q2.back()]<a[x]) q2.pop_back();
    q2.push_back(x);
}
int mx[N],mi[N];
signed main()
{

    int n, k; cin >> n >> k;
    for(int i=1;i<=n;i++) cin >> a[i];
    for(int i=1;i<k;i++) push(i);
    int ans=0,res=1;
    for(int i=k;i<=n;i++)
    {
        while(!q1.empty()&&q1.front()<i-k+1) q1.pop_front();
        while(!q2.empty()&&q2.front()<i-k+1) q2.pop_front();
        push(i);
        mi[i]=a[q1.front()],mx[i]=a[q2.front()];
        if(i>k&&mx[i]==a[i]&&mi[i-1]==a[i-k]) continue;
        if(q1.size()==k)
        {
            ans+=res,res=0; continue;
        }
        ans++;
    }
    cout<<ans<<endl;

    return 0;
}