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

/*
 public class _913C {

 }

 */
public class _913C {
  public void solve() throws FileNotFoundException {
    InputStream inputStream = System.in;

    InputHelper in = new InputHelper(inputStream);

    // actual solution
    int n = in.readInteger();

    long l = in.readInteger();

    long[] c = new long[n];

    for (int i = 0; i < n; i++) {
      c[i] = in.readInteger();
    }

    long[] oc = new long[n];

    oc[0] = c[0];

    for (int i = 1; i < n; i++) {
      oc[i] = Math.min(c[i], 2 * oc[i - 1]);
    }

    for (int i = n - 2; i >= 0; i--) {
      oc[i] = Math.min(oc[i], oc[i + 1]);
    }

    ans = rec(l, 0, oc, n - 1);

    System.out.println(ans);
    // end here
  }

  long ans = Long.MAX_VALUE;

  long rec(long l, long ans, long[] oc, int i) {
    if (i < 0) {
      return Long.MAX_VALUE;
    }

    long ti = 1 << i;

    long cl = l;

    ans += (cl / ti) * oc[i];

    cl -= (cl / ti) * ti;

    long nans = ans;

    if (cl > 0) {
      nans = Math.min(ans + oc[i], rec(cl, ans, oc, i - 1));
    }

    return nans;
  }

  public static void main(String[] args) throws FileNotFoundException {
    (new _913C()).solve();
  }

  class InputHelper {
    StringTokenizer tokenizer = null;
    private BufferedReader bufferedReader;

    public InputHelper(InputStream inputStream) {
      InputStreamReader inputStreamReader = new InputStreamReader(inputStream);
      bufferedReader = new BufferedReader(inputStreamReader, 16384);
    }

    public String read() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          String line = bufferedReader.readLine();
          if (line == null) {
            return null;
          }
          tokenizer = new StringTokenizer(line);
        } catch (IOException e) {
          e.printStackTrace();
        }
      }

      return tokenizer.nextToken();
    }

    public Integer readInteger() {
      return Integer.parseInt(read());
    }

    public Long readLong() {
      return Long.parseLong(read());
    }
  }
}
