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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep_in(i, s, n) for (int i = (s); i < (int)(n); i++)
typedef int64_t ll;

int main() {
  int n,k;
  cin>>n>>k;

  vector<int> p(n);
  rep(i,n){
    cin>>p[i];
  }

  set<int> s;
  rep(i,k){
    s.insert(p[i]);
  }
  int out=1;
  rep(i,n-k){
    s.insert(p[i+k]);
    if(*s.begin()!=p[i]||*s.rbegin()!=p[i+k]) out++;
    s.erase(p[i]);
  }

  cout<<out<<endl;
}