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: Wrong Answer)

use std::*;

#[allow(dead_code)]
fn read<T: str::FromStr>() -> T {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf.trim().parse().ok().unwrap()
}

#[allow(dead_code)]
fn read_vec<T: str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|a| a.parse().ok().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_vec2d<T: str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

// use std::collections::HashSet;
// use std::collections::HashMap;

fn main() {
    let v: Vec<usize> = read_vec();
    let (n, k) = (v[0], v[1]);
    let b: Vec<usize> = read_vec();
    let mut min_cost = usize::MAX;

    let mut tmp_max_b: Vec<usize> = Vec::new();
    let mut prev = b[0];
    for i in 0..b.len() {
        let tmp = cmp::max(prev, b[i]);
        tmp_max_b.push(tmp);
        prev = tmp;
    }

    let candidates: Vec<Vec<usize>> = (0..1 << n)
        .map(|bit| (0..n).filter(|i| bit & (1 << i) != 0).collect())
        .filter(|vec: &Vec<usize>| vec.len() == k)
        .collect();

    for cand in candidates {
        let mut cost = if cand[0] == 0 {
            0
        } else {
            tmp_max_b[cand[0]] + 1 - b[cand[0]]
        };
        let mut prev = if cand[0] == 0 {
            b[0]
        } else {
            tmp_max_b[cand[0]] + 1
        };
        for i in 1..cand.len() {
            if prev < b[cand[i]] {
                prev = b[cand[i]];
                continue;
            }
            prev += 1;
            cost += prev - b[cand[i]];
        }
        min_cost = cmp::min(cost, min_cost);
    }
    println!("{}", min_cost);
}