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.util.Collection;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Scanner;

public class P913C {
  public static void main(String[] args) {
    Scanner input = new Scanner(System.in);

    int n = input.nextInt();
    int L = input.nextInt();

    PriorityQueue<Node> nodes = new PriorityQueue<>(Comparator.comparing(Node::density));
    int power = 1;
    for (int i = 0; i < n; i++) {
      nodes.add(new Node(input.nextInt(), power));
      power *= 2;
    }

    System.out.println(getMin(nodes, L));
  }

  private static long getMin(PriorityQueue<Node> nodes, int l) {
    if (l <= 0) return 0;

    Node cur = nodes.poll();
    long ans = ((long)l / cur.vol) * cur.cost;
    int rem = l % cur.vol;
    return rem == 0 ? ans : ans + Math.min(getMin(nodes, rem), cur.cost);
  }


  private static class Node {
    private final int cost;
    private final int vol;

    private Node(int cost, int vol) {
      this.cost = cost;
      this.vol = vol;
    }

    public double density() {

      return cost * 1.0 / vol;
    }

    @Override
    public String toString() {
      return "Node{" +
        "cost=" + cost +
        ", vol=" + vol +
        '}';
    }
  }
}
