Problem:
Max Score: 350 Points

Problem Statement

There are N buildings along the line. The i-th building from the left is colored in color i, and its height is currently a_i meters.

Chokudai is a mayor of the city, and he loves colorful thigs. And now he wants to see at least K buildings from the left.

You can increase height of buildings, but it costs 1 yens to increase 1 meters. It means you cannot make building that height is not integer.

You cannot decrease height of buildings.

Calculate the minimum cost of satisfying Chokudai's objective.

Note: "Building i can see from the left" means there are no j exists that (height of building j) ≥ (height of building i) and j < i.

Input Format

N K
a_1 a_2 a_3 ... a_N

Output Format

Print the minimum cost in one line. In the end put a line break.

Constraints

1 ≤ K ≤ N ≤ 15

1 ≤ a_i ≤ 10^9

Scoring

Subtask 1 [120 points]

N = K

Subtask 2 [90 points]

N ≤ 5

a_i ≤ 7

Subtask 3 [140 points]

There are no additional constraints.

Sample Input 1

5 5
3949 3774 3598 3469 3424

Sample Output 1

1541

The optimal solution is (height of buildings from the left) = [3949, 3950, 3951, 3952, 3953].

Sample Input 2

5 3
7 4 2 6 4

Sample Output 2

7

The optimal solution is (height of buildings from the left) = [7, 8, 2, 9, 4].

Solution in PHP7 (7.0.15) (judge verdict: Accepted)

<?php
fscanf(STDIN, "%d %d", $n, $k);
$a = explode(' ', trim(fgets(STDIN)));
$c = $h = 0;
foreach ($a as $b) {
	if ($h < $b) {
		$c++;
		$h = $b;
	}
}
if ($c >= $k) exit("0\n");
$ps[0][] = [0, $a[0], 1];
$x = PHP_INT_MAX;
for ($i = 1; $i < $n; $i++) {
	foreach ($ps[$i-1] as $p) {
		if ($a[$i] > $p[1]) {
			if ($p[2] + 1 == $k) {
				if ($x > $p[0]) $x = $p[0];
			} else {
				$ps[$i][] = [$p[0], $a[$i], $p[2] + 1];
			}
		} else {
			if ($p[2] + ($n - $i) > $k) $ps[$i][] = $p;
			$cost = $p[0] + $p[1] - $a[$i] + 1;
			if ($p[2] + 1 == $k) {
				if ($x > $cost) $x = $cost;
			} else {
				$ps[$i][] = [$cost, $p[1] + 1, $p[2] + 1];
			}
		}
	}
}
echo $x, "\n";