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;
use std::cmp::min;

fn main() {
    input! {
        n: usize,
        k: usize,
        height: [usize; n],
    }
    let mut res: usize = 1_000_000_000_000;

    for bit in 0..1 << n {
        let mut col: usize = 0;
        let mut budget: usize = 0;
        let mut now_h: usize = 0;
        for i in 0..n {
            if now_h < height[i] {
                now_h = height[i];
                col += 1;
            } else if bit & (1 << i) > 0 {
                now_h += 1;
                budget += now_h - height[i];
                col += 1;
            }
        }
        if col >= k {
            res = min(res, budget);
        }
    }

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