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.*;
import java.io.*;

public class C {
	
	class Bottle{
		int price;
		int quantity;
		float rate;
	}
	static Bottle[] b;
	static int l;
	
	public static long calculate(int i)
	{
		long ans=0;
		//System.out.println(i+" "+b[i].price);
		while(l!=0)
		{
			if(b[i].quantity<=l)
			{
				int quantity = l/b[i].quantity;
				ans+=(long)b[i].price*(long)quantity;
				l-=b[i].quantity*quantity;
				//System.out.println("if");
			}
			else
			{
				//System.out.println("else "+b[i].price+" "+i);
				return ans+=Math.min(b[i].price,calculate(i-1));
			}
			
		}
		//System.out.println(ans);
		return ans;
	}
	
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		C c = new C();
		int n = sc.nextInt();
		l = sc.nextInt();
		b = new Bottle[n];
		b[0] = c.new Bottle();
		b[0].price=sc.nextInt();
		b[0].quantity=(int) Math.pow(2, 0);
		b[0].rate = (float) (b[0].price/(b[0].quantity*1.0));
		for(int i=1;i<n;i++)
		{
			b[i] = c.new Bottle();
			b[i].price=sc.nextInt();
			b[i].quantity=(int) Math.pow(2, i);
			b[i].rate = (float) (b[i].price/(b[i].quantity*1.0));
			b[i].price = Math.min(b[i].price, 2*b[i-1].price);
		}
		long ans = calculate(n-1);
		out.println(ans);
		sc.close();
		out.close();
	}
	static void debug(Object...obj)
	{
		System.out.println(Arrays.deepToString(obj));
	}
}
