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::cmp::max as max;
use std::cmp::min as min;

use itertools::Itertools;

fn build(buildings: &Vec<u64>, build_ups: &Vec<u64>) -> u64 {
    //println!("{:?}", build_ups);
    let mut highest = buildings[0] - 1;
    let mut costs = 0;

    for i in 0..buildings.len() {
        //print!("{}: ", i);
        //print!("highest: {} ", highest);
        let cost = if build_ups.contains(&(i as u64)) {
            //print!("( if ) ");
            if highest + 1 < buildings[i] { 0 } else { highest + 1 - buildings[i] }
        } else {
            //print!("( else ) ");
            0
        };
        costs += cost;
        highest = max(highest, buildings[i] + cost);
        //print!("highest: {} ", highest);
        //println!("cost: {}\n", cost);
    }
    //println!("------");
    costs
}

fn solve(buildings: Vec<u64>, n: usize, k: usize) -> u64 {
    let mut result = 9223372036854775807;

    for build_ups in (0..n as u64).combinations(k) {
        result = min(build(&buildings, &build_ups), result)
    }

    result
}

fn main() {
//    let (n, k) = (5, 3);
//    let buildings = vec![4, 4, 2, 6, 4];
    let (n, k) = read_tup2();
    let buildings = read_vec();

    println!("{}", solve(buildings, n, k));
}

// utils

fn read_tup2<T: std::str::FromStr + Copy>() -> (T, T) {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    let v = s.trim().split_whitespace()
        .map(|c| c.parse().ok().unwrap())
        .collect::<Vec<T>>();
    (v[0], v[1])
}

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(|c| c.parse().ok().unwrap())
        .collect()
}