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

function fget_array($dlmt = null) {
    $input = trim(fgets(STDIN));
    return $dlmt ? explode($dlmt, $input) : str_split($input);
}

list($n, $k) = fget_array(' ');
$p = fget_array(' ');

$lastI = -$k;
$lastC = 0;
$offset = 0;
$prev = $p[0];
$list = [];

for ($i = 1; $i < $n; $i++) {
    $curr = $p[$i];
    if ($prev > $curr) {
        $list[] = $lastC = $i - $lastI;
        $lastI = $i;
    }
    if ($lastI > 1 && $lastC < $k - 1) {
        #print_r(compact('i', 'lastI', 'lastC'));
        $offset++;
    }
    $prev = $curr;
}
#print_r($list);
$list = array_filter($list, function($cnt) use ($k) { return $cnt + 1 >= $k; });
print_r($offset + count($list));
?>