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

public class Main{
    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int n = fs.nextInt();
        int k = fs.nextInt();
        int[] a = new int[n];
        int[] temp = new int[n];
        for(int i=0;i<n;i++){
            a[i] = fs.nextInt();
        }
        int count;
        long min = 1000000000000L;
        for(int i=0;i<(1<<n);i++){
            count = Integer.bitCount(i);
            if(count<k)continue;

            for(int j=0;j<n;j++){
                temp[j] = a[j];
            }
            int prevMaxHeight = temp[0];
            long price = 0;
            int diff ;
            for(int j=1;j<n;j++){
                if(((i>>j)&1)==1){
                    diff = Math.max(0,prevMaxHeight-temp[j]+1);
                    temp[j]+=diff;
                    price += diff;

                }
                prevMaxHeight = Math.max(prevMaxHeight,temp[j]);
            }
            min = Math.min(price,min);
        }
        System.out.println(min);
    }

    static class FastScanner {
            private final InputStream in = System.in;
            private final byte[] buffer = new byte[1024];
            private int ptr = 0;
            private int buflen = 0;
            private boolean hasNextByte() {
                if (ptr < buflen) {
                    return true;
                }else{
                    ptr = 0;
                    try {
                        buflen = in.read(buffer);
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                    if (buflen <= 0) {
                        return false;
                    }
                }
                return true;
            }
            private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
            private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
            public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
            public String next() {
                if (!hasNext()) throw new NoSuchElementException();
                StringBuilder sb = new StringBuilder();
                int b = readByte();
                while(isPrintableChar(b)) {
                    sb.appendCodePoint(b);
                    b = readByte();
                }
                return sb.toString();
            }
            public long nextLong() {
                if (!hasNext()) throw new NoSuchElementException();
                long n = 0;
                boolean minus = false;
                int b = readByte();
                if (b == '-') {
                    minus = true;
                    b = readByte();
                }
                if (b < '0' || '9' < b) {
                    throw new NumberFormatException();
                }
                while(true){
                    if ('0' <= b && b <= '9') {
                        n *= 10;
                        n += b - '0';
                    }else if(b == -1 || !isPrintableChar(b)){
                        return minus ? -n : n;
                    }else{
                        throw new NumberFormatException();
                    }
                    b = readByte();
                }
            }
            public int nextInt() {
                long nl = nextLong();
                if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
                return (int) nl;
            }
            public double nextDouble() { return Double.parseDouble(next());}
        }
}