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.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            long l = in.nextInt();
            long[] c = new long[n];
            for (int i = 0; i < n; i++)
                c[i] = in.nextInt();
            int sz = 33;
            long[] dp = new long[sz];
            dp[0] = c[0];
            for (int i = 1; i < sz; i++)
                if (i < n)
                    dp[i] = Math.min(c[i], 2 * dp[i - 1]);
                else
                    dp[i] = 2 * dp[i - 1];
            for (int i = sz - 2; i >= 0; i--)
                dp[i] = Math.min(dp[i], dp[i + 1]);
            long ans = Long.MAX_VALUE;
            boolean f = true;
            for (int r = sz - 1; r >= 0; r--) {
                long v = 1L << r;
                long cr = l & v;
                if (cr == 0L && f)
                    ans = Math.min(ans, dp[r]);
                else {
                    if (cr > 0)
                        f = false;
                    else {
                        long t = l;
                        int pos = 0;
                        long curAns = 0L;
                        while (t > 0) {
                            if (pos == r)
                                curAns += dp[pos];
                            else if (pos > r)
                                curAns += (t % 2L) * dp[pos];
                            t /= 2;
                            pos++;
                        }
                        ans = Math.min(ans, curAns);
                    }
                }
            }
            long eqL = 0L;
            for (int i = 0; i < sz; i++)
                if ((l & (1L << i)) > 0)
                    eqL += dp[i];
            ans = Math.min(ans, eqL);
            out.println(ans);
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}

