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
fscanf(STDIN, "%d %d", $n, $k);
$p = array_map('intval', explode(' ', trim(fgets(STDIN))));
$c = 0; $max = 200000; $min = -1; $f = true;
for ($i=0; $i < $n - $k + 1; $i++) {
    $t = array_slice($p, $i, $k);
    $max = max($t);
    if ($f) {
        $ts = $t;
        sort($ts, SORT_NUMERIC);
        if ($ts !== $t) {
            $c++;
            $f = false;
        }
    } else {
        if($p[$i - 1] !== $min || $p[$i + $k - 1] !== $max) $c++;
    }
    $min = min($t);
}
echo $c;
?>