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.

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.

Input Format


N K
a_1 a_2 a_3 ... a_N

Example

Input

5 5
3949 3774 3598 3469 3424


Output

1541
import java.io.*;
import java.util.*;

public class Main {
    static ContestScanner in;
    static Writer out;
    public static void main(String[] args) {
        Main main = new Main();
        try {
            in = new ContestScanner();
            out = new Writer();
            main.solve();
            out.close();
            in.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    void solve() throws IOException {
        int n = in.nextInt();
        int k = in.nextInt();
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }
        int sz = 1 << n;
        long min = Long.MAX_VALUE;
        for (int i = 0; i < sz; i++) {
            long cost = 0;
            long pre = 0;
            int cnt = 0;
            for (int j = 0; j < n; j++) {
                if(a[j] > pre) cnt++;
                if((i & 1 << j) > 0) {
                    long add = pre < a[j] ? 0 : pre + 1 - a[j];
                    cost += add;
                    if(add > 0) cnt++;
                    pre++;
                }
                pre = Math.max(pre, a[j]);
            }
            if(cnt < k) continue;
            min = Math.min(min, cost);
        }
        System.out.println(min);
    }
}

@SuppressWarnings("serial")
class MultiSet<T> extends HashMap<T, Long>{
    @Override public Long get(Object key){return containsKey(key)?super.get(key):0L;}
    public void add(T key,long v){put(key,get(key)+v);}
    public void add(T key){put(key,get(key)+1);}
    public void sub(T key){final long v=get(key);if(v==1)remove(key);else put(key,v-1);}
    public MultiSet<T> merge(MultiSet<T> set)
    {MultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
        for(Entry<T,Long>e:s.entrySet())l.add(e.getKey(),e.getValue());return l;}
}

class Writer extends PrintWriter{
    public Writer(String filename)throws IOException
    {super(new BufferedWriter(new FileWriter(filename)));}
    public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
    private BufferedReader in;private int c=-2;
    public ContestScanner()throws IOException
    {in=new BufferedReader(new InputStreamReader(System.in));}
    public ContestScanner(String filename)throws IOException
    {in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
    public String nextToken()throws IOException {
        StringBuilder sb=new StringBuilder();
        while((c=in.read())!=-1&&Character.isWhitespace(c));
        while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
        return sb.toString();
    }
    public String readLine()throws IOException{
        StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
        while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
        return sb.toString();
    }
    public long nextLong()throws IOException,NumberFormatException
    {return Long.parseLong(nextToken());}
    public int nextInt()throws NumberFormatException,IOException
    {return(int)nextLong();}
    public double nextDouble()throws NumberFormatException,IOException
    {return Double.parseDouble(nextToken());}
    public void close() throws IOException {in.close();}
}
