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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::{input, fastout};

#[fastout]
fn main() {
    input!{
        n: usize,
        k: usize,
        a: [usize; n]
    }

    let mut min_cost = std::usize::MAX;
    for bit in 0..(1 << n) {
        let mut min_height = a[0];
        let mut color_num = 1;
        let mut cost = 0;
        for i in 1..n {
            if color_num == k {
                break;
            }
            if min_height < a[i] {
                min_height = a[i];
                color_num += 1;
            } else {
                if (bit >> i) & 1 == 1 {
                    // min_heightより1高くする
                    cost += (min_height + 1) - a[i];
                    min_height = min_height + 1;
                    color_num += 1;
                }
            }
        }

        if color_num == k {
            min_cost = min_cost.min(cost);
        }
    }
    println!("{}", min_cost);
}