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 Solution{

	
	static class Node implements Comparable<Node>{
		int c,v;
		Node(int c,int v){
			this.c=c;
			this.v=v;
		}

		public int compareTo(Node obj){
			double v1=(double)this.c/this.v;
			double v2=(double)obj.c/obj.v;

			if(v1<=v2)
				return -1;
			else
				return 1;
		}

		public String toString(){
			return c+" "+v+" "+(float)c/v;
		}
	}


	public static void main(String args[]){

		Scanner in=new Scanner(new BufferedReader(new InputStreamReader(System.in)));

		int n=in.nextInt();
		long l=in.nextInt();

		ArrayList<Node> list=new ArrayList<>();
		for(int i=0;i<n;i++)
			list.add( new Node(in.nextInt(),1<<i) );


		Collections.sort(list);
		//System.out.println(list);


		System.out.println( minimum(l, list) );
	}


	public static long minimum(long l, ArrayList<Node> list){
		if(l==0)
			return 0;

		long zerocost=Long.MAX_VALUE;

		int i;
		for(i=0; i<list.size(); i++)
			if(list.get(i).v>=l)
				zerocost=Math.min(zerocost,list.get(i).c);
			else
				break;

		if(i==list.size())
			return zerocost;
		else
			return Math.min( zerocost, l/list.get(i).v*list.get(i).c + minimum(l%list.get(i).v, list) );
	}

}