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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    static InputStream is;
    static PrintWriter out;
    static String INPUT = "";

    static void solve() {
        // Initialize.
        int N = ni();
        int K = ni();
        int[] buildings = new int[N];
        for (int i = 0; i < N; i++) {
            buildings[i] = ni();
        }
        // Bit 全探索
        long min = Long.MAX_VALUE;
        for (int bit = 0; bit < (1 << N); bit++) {
            // K 個以上のビルが見える時のパターンのみ探索。
            if (Integer.bitCount(bit) >= K) {
                int currentMax = 0;
                long add = 0;
                for (int i = 0; i < N; i++) {
                    // 見える・見えないビルについて高さの検証。
                    // 見える場合は、前のビルより高さを+1大きくするないし
                    // すでに高い場合はそのままにする。
                    // 見えない場合は現時点で最高の高さを更新する。
                    if ((bit & (1 << i)) != 0) {
                        add += Math.max(0, currentMax - buildings[i] + 1);
                        currentMax = Math.max(currentMax + 1, buildings[i]);
                    } else {
                        currentMax = Math.max(currentMax, buildings[i]);
                    }
                }
                min = Math.min(min, add);
            }
        }

        out.println(min);
    }

    public static void main(String[] args) throws Exception {
        long S = System.currentTimeMillis();
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);

        solve();
        out.flush();
        long G = System.currentTimeMillis();
        tr(G-S+"ms");
    }

    private static boolean eof() {
        if(lenbuf == -1)return true;
        int lptr = ptrbuf;
        while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;

        try {
            is.mark(1000);
            while(true){
                int b = is.read();
                if(b == -1){
                    is.reset();
                    return true;
                }else if(!isSpaceChar(b)){
                    is.reset();
                    return false;
                }
            }
        } catch (IOException e) {
            return true;
        }
    }

    private static byte[] inbuf = new byte[1024];
    static int lenbuf = 0, ptrbuf = 0;

    private static int readByte() {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }

    private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }

    private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

    private static double nd() { return Double.parseDouble(ns()); }
    private static char nc() { return (char)skip(); }

    private static String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private static char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private static char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }

    private static int[] na(int n) {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }

    private static int ni() {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private static long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }

    // Union-Find
    // https://algs4.cs.princeton.edu/15uf/UF.java.html
    public static class UnionFind {
        private int count = 0;
        private int[] parent, rank;

        public UnionFind(int n) {
            count = n;
            parent = new int[n];
            rank = new int[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
            }
        }

        public int find(int p) {
            while (p != parent[p]) {
                parent[p] = parent[parent[p]];
                p = parent[p];
            }
            return p;
        }

        public void union(int p, int q) {
            int rootP = find(p);
            int rootQ = find(q);
            if (rootP ==rootQ) return;
            if (rank[rootQ] > rank[rootP]) {
                parent[rootP] = rootQ;
            } else {
                parent[rootQ] = rootP;
                if (rank[rootP] == rank[rootQ]) {
                    rank[rootP]++;
                }
            }
            count--;
        }

        public int count() {
            return count;
        }

        public void print() {
            out.println("Parent:");
            for (int i : parent) {
                out.print(i);
                out.print(" ");
            }
            out.println();
            out.println("Rank:");
            for (int i : rank) {
                out.print(i);
                out.print(" ");
            }
            out.println();
        }
    }

    // Dijkstra
    // Return min distance from start to end O(ElogV) (negative cost is prohibited)
    // edge is int[3] array {from,to,cost}
    // edges is edge list from specific node
    // all_edges is Map<from node number,edges>
    static int dijkstra(Map<Integer,List<int[]>> all_edges,int start,int end,int max_node_number) {
        int[] distance = new int[max_node_number + 1];
        Arrays.fill(distance, -1);
        PriorityQueue<int[]> p_que = new PriorityQueue<>((a,b) -> ((distance[a[0]] + a[2]) - (distance[b[0]] + b[2])));
        distance[start] = 0;
        List<int[]> edges = all_edges.get(start);
        p_que.addAll(edges);
        while (distance[end] < 0) {
            int[] nearest_edge = p_que.poll();
            assert nearest_edge != null;
            if (distance[nearest_edge[1]] < 0) {
                distance[nearest_edge[1]] = distance[nearest_edge[0]] + nearest_edge[2];
                if (all_edges.containsKey(nearest_edge[1])) {
                    edges = all_edges.get(nearest_edge[1]);
                    for (int[] edge : edges) {
                        if (distance[edge[1]] < 0) p_que.add(edge);
                    }
                }
            }
        }
        return distance[end];
    }

    // Enumerate primes in [2, n] with O(n log log n)
    public static List<Integer> sieveOfEratosthenes(int n) {
        boolean[] isPrime = new boolean[n+1];
        Arrays.fill(isPrime, true);
        for (int i = 2; i * i <= n; i++) {
            if (isPrime[i]) {
                for (int j = i + i; j <= n; j += i) {
                    isPrime[j] = false;
                }
            }
        }
        List<Integer> primes = new ArrayList<>();
        for (int i = 2; i <= n; i++) {
            if (isPrime[i]) {
                primes.add(i);
            }
        }
        return primes;
    }

    // Count divisor
    public static int countDivisor(int n) {
        int[] list = new int[n + 1];
        Arrays.fill(list, 0);
        int num = n;
        for (int i = 2; i <= n; i++) {
            while (num % i == 0) {
                list[i] = list[i] + 1;
                num /= i;
            }
        }
        int ans = 1;
        for (int i : list) {
            ans *= (i + 1);
        }
        return ans;
    }
}
