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 <algorithm>
#include <cmath>
#include <cstdio>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_set>
#include <vector>

using namespace std;

#define FOR(i, N) for (int i = 0; i < (int)N; i++)
#define FORIN(i, a, b) for (int i = a; i < (int)b; i++)
#define ALL(x) (x).begin(), (x).end()
#define MOD 1000000007
#define DEBUG(...) debug(__LINE__, ":" __VA_ARGS__)

using Pi = pair<int, int>;
using ll = long long;
const int INF = 1 << 28;

string to_string(string s) {
  return s;
}

template<class S,class T>
string to_string(pair<S,T> p){
	return "{"+to_string(p.first)+","+to_string(p.second)+"}";
}

template <class T>
string to_string(unordered_set<T> s){
	string ret="{";
	for(T t:s)ret+=to_string(t)+",";
	ret+="}";
	return ret;
}

template <class T>
string to_string(vector<T> v) {
  string ret = "{";
  for (int i = 0; i < (int)v.size() - 1; ++i) {
    ret += to_string(v[i]) + ",";
  }
  if (v.size() > 0) {
    ret += to_string(v.back());
  }
  ret += "}";
  return ret;
}

void debug() {
  cerr << endl;
}

template <class Head, class... Tail>
void debug(Head head, Tail... tail) {
  cerr << to_string(head) << " ";
  debug(tail...);
}

void print() {
  cout << endl;
}

template <class Head, class... Tail>
void print(Head head, Tail... tail) {
  cout << to_string(head);
  print(tail...);
}

int main() {
  int N,K;
  cin>>N>>K;
  vector<int> P(N);
  FOR(i,N)cin>>P[i];
  int ans=N+1-K;
  FORIN(i,1,N-K+1){
	  if(P[i-1]<P[i]&&P[i+K-2]<P[i+K-1])ans--;
  }
  print(ans);
  return 0;
}