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 (1.15.1) (judge verdict: Accepted)

use std::cmp::min;


fn main() {
    let (n, k) = read_tuple::<usize>();
    let an: Vec<i64> = read_vec();

    let mut ans = i64::max_value();
    for i in 0..(1<<n) {
        if i % 2 != 1 || ((i as usize).count_ones() as usize) < k {
            continue;
        }

        let mut an = an.clone();
        let mut max_height = an[0];
        let mut cost = 0;
        for j in 1..n {
            if i & (1 << j) == (1 << j) {
                if an[j] <= max_height {
                    cost += max_height - an[j] + 1;
                    an[j] = max_height + 1;
                    max_height += 1;
                } else {
                    // an[j] > max_height
                    max_height = an[j];
                }
            } else {
                if max_height < an[j] {
                    cost = i64::max_value();
                    break;
                }
            }
        }

        ans = min(ans, cost);
    }

    println!("{}", ans);
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

fn read_tuple<T: std::str::FromStr + Copy>() -> (T, T) {
    let temp = read_vec();
    (temp[0], temp[1])
}