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 std::io;
use std::cmp;

fn main() {
    let (n, k) = {
        let i = read::<usize>();
        (i[0], i[1] as u32)
    };
    let an = read::<usize>();

    let mut ans = std::usize::MAX;
    for b in 0..1 << n {
        if (b as usize).count_ones() < k { continue; }
        let mut h = an[0];
        let mut cost: usize = 0;
        for i in 0..n {
            if b & (1 << i) != 0 {
                if i != 0 && h >= an[i] {
                    cost += h - an[i] + 1;
                    h += 1;
                }
            }
            h = cmp::max(h, an[i]);
        }
        ans = cmp::min(ans, cost);
    }

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

#[allow(unused)]
fn read<T>() -> Vec<T>
where
    T: std::str::FromStr,
    T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.split_whitespace()
        .map(|s| s.trim().parse().unwrap())
        .collect()
}


#[allow(unused)]
fn read_one<T>() -> T
where
    T: std::str::FromStr,
    T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim().parse().unwrap()
}