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::*;
use std::io::Read;
use std::iter::Scan;

trait Ext {
    fn try_fold_<B, F>(&mut self, init: B, mut f: F) -> Option<B>
    where
        Self: Sized + Iterator,
        F: FnMut(B, Self::Item) -> Option<B>,
    {
        let mut accum = init;
        while let Some(x) = self.next() {
            if let Some(new_accum) = f(accum, x) {
                accum = new_accum;
            } else {
                return None;
            }
        }
        Some(accum)
    }
}
impl<I, St, F> Ext for Scan<I, St, F> {}

fn cost(a: &[i64], bits: u32) -> Option<i64> {
    a.iter()
        .enumerate()
        .scan(0, |cur_height, (i, &height)| {
            let (next_height, expected_height) = if (bits >> i) & 1 != 0 {
                (max(*cur_height + 1, height), max(*cur_height + 1, height))
            } else {
                (*cur_height, min(*cur_height, height))
            };
            *cur_height = next_height;
            Some((height, expected_height))
        })
        .try_fold_(0, |cost, (height, expected_height)| {
            if height > expected_height {
                None
            } else {
                Some(cost + expected_height - height)
            }
        })
}

fn solve(n: usize, k: usize, a: Vec<i64>) -> i64 {
    (0u32..(1 << n))
        .filter(|&bits| bits.count_ones() >= (k as u32))
        .filter_map(|bits| cost(&a, bits))
        .min()
        .unwrap()
}

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();
    let k: usize = iter.next().unwrap().parse().unwrap();
    let a = (0..n)
        .map(|_| iter.next().unwrap().parse().unwrap())
        .collect();
    let r = solve(n, k, a);
    println!("{}", r);
}