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

public class CHello2018
{
    public static void main(String[] args)
    {
        new CHello2018(System.in, System.out);
    }

    private static class Solver implements Runnable
    {
        int n, l;
        long[] costs;
        InputReader in;
        PrintWriter out;

        void solve() throws IOException
        {
            n = in.nextInt();
            l = in.nextInt();
            costs = new long[32];

            Arrays.fill(costs, -1);

            for (int i = 0; i < n; i++)
                costs[i] = in.nextInt();

            for (int i = 1; i < 32; i++)
            {
                if (costs[i] == -1)
                    costs[i] = costs[i - 1] << 1;
                else
                    costs[i] = Math.min(costs[i], costs[i - 1] << 1);
            }

            long ans = 0;

            for (int i = 0; i < 32; i++)
            {
                if (costs[i] < ans)
                    ans = costs[i];

                if ((l & (1 << i)) > 0)
                    ans += costs[i];
            }

            out.println(ans);
        }

        Solver(InputReader in, PrintWriter out)
        {
            this.in = in;
            this.out = out;
        }

        @Override
        public void run()
        {
            try
            {
                solve();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
        }

    }

    private static class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        int read()
        {
            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars)
            {
                curChar = 0;
                try
                {
                    numChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }

            return buf[curChar++];
        }

        int nextInt()
        {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-')
            {
                sgn = -1;
                c = read();
            }

            int res = 0;

            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();

                res *= 10;
                res += c & 15;

                c = read();
            } while (!isSpaceChar(c));

            return res * sgn;
        }

        boolean isSpaceChar(int c)
        {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        void close()
        {
            try
            {
                stream.close();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
        }

        InputReader(InputStream stream)
        {
            this.stream = stream;
        }

    }

    private CHello2018(InputStream inputStream, OutputStream outputStream)
    {
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Thread thread = new Thread(null, new Solver(in, out), "Solver", 1 << 29);

        try
        {
            thread.start();
            thread.join();
        }
        catch (InterruptedException e)
        {
            e.printStackTrace();
        }

        in.close();
        out.flush();
        out.close();
    }

}
