A New Year party is not a New Year party without lemonade! As usual, you are expecting a lot of guests, and buying lemonade has already become a pleasant necessity.

Your favorite store sells lemonade in bottles of n different volumes at different costs. A single bottle of type i has volume 2i - 1 liters and costs ci roubles. The number of bottles of each type in the store can be considered infinite.

You want to buy at least L liters of lemonade. How many roubles do you have to spend?

Input

The first line contains two integers n and L (1 ≤ n ≤ 30; 1 ≤ L ≤ 109) — the number of types of bottles in the store and the required amount of lemonade in liters, respectively.

The second line contains n integers c1, c2, ..., cn (1 ≤ ci ≤ 109) — the costs of bottles of different types.

Output

Output a single integer — the smallest number of roubles you have to pay in order to buy at least L liters of lemonade.

Examples

Input

4 12
20 30 70 90


Output

150


Input

4 3
10000 1000 100 10


Output

10


Input

4 3
10 100 1000 10000


Output

30


Input

5 787787787
123456789 234567890 345678901 456789012 987654321


Output

44981600785557577

Note

In the first example you should buy one 8-liter bottle for 90 roubles and two 2-liter bottles for 30 roubles each. In total you'll get 12 liters of lemonade for just 150 roubles.

In the second example, even though you need only 3 liters, it's cheaper to buy a single 8-liter bottle for 10 roubles.

In the third example it's best to buy three 1-liter bottles for 10 roubles each, getting three liters for 30 roubles.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;


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


    static class TaskC {
        long[] c;
        int n;

        long best(int L) {
            long minCost = Long.MAX_VALUE;
            for (int i = 0; i < n; i++) {
                if (1L << i >= L) {
                    minCost = Math.min(minCost, c[i]);
                }
            }
            for (int i = n - 1; i >= 0; i--) {
                if (1L << i >= L) {
                    continue;
                }
                if (minCost > c[i])
                    minCost = Math.min(minCost, c[i] + best(L - (1 << i)));
                break;
            }
            return minCost;
        }

        void Solve(InputReader in, PrintWriter out) {
            n = in.NextInt();
            int L = in.NextInt();
            c = new long[30];
            c[0] = in.NextInt();
            for (int i = 1; i < n; i++) {
                c[i] = Math.min(2 * c[i - 1], in.NextInt());
            }
            for (int i = n; i < 30; i++) {
                c[i] = 2 * c[i - 1];
            }
            n = 30;
            out.println(best(L));
        }

        static int GetMax(int[] ar) {
            int max = Integer.MIN_VALUE;
            for (int a : ar) {
                max = Math.max(max, a);
            }
            return max;
        }

        static int GetMin(int[] ar) {
            int min = Integer.MAX_VALUE;
            for (int a : ar) {
                min = Math.min(min, a);
            }
            return min;
        }

        static long GetSum(int[] ar) {
            long s = 0;
            for (int a : ar) s += a;
            return s;
        }

        static int[] GetCount(int[] ar) {
            return GetCount(ar, GetMax(ar));
        }

        static int[] GetCount(int[] ar, int maxValue) {
            int[] dp = new int[maxValue + 1];
            for (int a : ar) {
                dp[a]++;
            }
            return dp;
        }

        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(), " \t\n\r\f,");
                    } catch (IOException e) {
                        throw new RuntimeException(e);
                    }
                }
                return tokenizer.nextToken();
            }

            int NextInt() {
                return Integer.parseInt(Next());
            }

            long NextLong() {
                return Long.parseLong(Next());
            }

            double NextDouble() {
                return Double.parseDouble(Next());
            }

            int[] NextIntArray(int n) {
                return NextIntArray(n, 0);
            }

            int[] NextIntArray(int n, int offset) {
                int[] a = new int[n];
                for (int i = 0; i < n; i++) {
                    a[i] = NextInt() - offset;
                }
                return a;
            }

            int[][] NextIntMatrix(int n, int m) {
                return NextIntMatrix(n, m, 0);
            }

            int[][] NextIntMatrix(int n, int m, int offset) {
                int[][] a = new int[n][m];
                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < m; j++) {
                        a[i][j] = NextInt() - offset;
                    }
                }
                return a;
            }
        }
    }
}
