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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
list($n,$k)=explode(" ",trim(fgets(STDIN)));
if($k==$n){
  echo 1;
}else{
  //これは嘘
  $p=explode(" ",trim(fgets(STDIN)));
  $ans=$n-$k;
  $i=$k-1;
  $r=$p[$k-1];
  $c=0;
  while($i<$n){
    if($r<$p[$i]){
      ++$c;
    }else{
      $c=0;
    }
    if($c>=$k){
      --$ans;
    }
    $r=$p[$i];
    ++$i;
  }
  echo $ans;
}