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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;
import java.awt.Point;

public class Main {
    static int INF = (1 << 30) - 1;
    // static long L_INF = (1L << 62) - 1;
    // static long MOD = (long) 1e9 + 7;

    static class Solver {
        int N, K;
        int[] A;

        // write your code
        void solve(InputReader in, PrintWriter out) {
            N = in.nextInt();
            K = in.nextInt();
            A = new int[N];
            for (int i = 0; i < N; i++) {
                A[i] = in.nextInt();
            }

            int[] maxes = new int[N + 1];
            for (int i = 0; i < N; i++) {
                maxes[i + 1] = Math.max(maxes[i], A[i]);
            }

            int ans = INF;
            for (int i = 0; i < (1 << N); i++) {
                if (Integer.bitCount(i) != K) {
                    continue;
                }
                ArrayList<Integer> al = new ArrayList<>();
                int bit = i;
                int d = 0;
                while (bit > 0) {
                    if ((bit & 1) == 1) {
                        al.add(d);
                    }
                    bit /= 2;
                    d++;
                }
                int cost = 0;
                int before = 0;
                for (int j = 0; j < al.size(); j++) {
                    int idx = al.get(j);
                    int v = A[idx];
                    if (v <= Math.max(before, maxes[idx])) {
                        cost += Math.max(before, maxes[idx]) - v + 1;
                        before = Math.max(before, maxes[idx]) + 1;
                    }
                }
                ans = Math.min(ans, cost);
            }
            out.println(ans);
        }

        void debug(Object... os) {
            System.err.println(Arrays.deepToString(os));
        }
    }

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(in, out);
        out.close();
    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}