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.io.IOException;
import java.io.InputStreamReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author ShekharN
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        long[] cost = new long[32];

        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt(), l = in.nextInt();

            int id = -1;
            long mn = Long.MAX_VALUE;
            for (int i = 0; i < n; i++) {
                cost[i] = in.nextInt();
            }

        /*for (int i = 0; i <= id; i++) {
            cost[i] = mn;
        }*/

            for (int j = 0; j < n; j++) {
                if (j != 0) cost[j] = Long.min(cost[j], cost[j - 1] * 2);
            }


            for (int i = n; i < 31; i++) {
                cost[i] = 2 * cost[i - 1];
            }

            for (int i = 30; i >= 0; i--) {
                mn = Math.min(mn, cost[i]);
                cost[i] = mn;
            }

            long ans = fun(l);
            out.println(ans);
        /*for (int i = 0; i <= 30; i++) {
            if(((1<<i) & l) != 0)
                out.print("1");
            else out.print("0");
        }*/
        }

        private long fun(int l) {
            if (l <= 0) return 0;
            for (int i = 30; i >= 0; i--) {
                if ((l & (1 << i)) != 0) {
                    return Math.min(fun(l - (1 << i)) + cost[i], cost[i + 1]);
                }
            }
            return 0;
        }

    }

    static class FastScanner {
        private BufferedReader br;
        private StringTokenizer st;

        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        public String nextString() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextString());
        }

    }
}

