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.Scanner;

public class partyLemonade {
	
	
	
	public static long minPrice(int volreq,int n,int[] price)
	{
		int temp=volreq;
		for(int i=0;i<n-1;i++)
		{
			if(price[i]*2<price[i+1])
				price[i+1]=price[i]*2;
		}
		
		for(int i=n-1;i>0;i--)
		{
			if(price[i]<price[i-1])
		
				price[i-1]=price[i];
		}
		
	/*	for(int i=0;i<n;i++)
			System.out.print(price[i]+" ");*/

		/*System.out.println();*/
		if(volreq%(Math.pow(2, n-1))==0)
			return price[n-1]*(volreq/(long)Math.pow(2, n-1));
		
		long totprice=0;
		totprice+=price[n-1]*(long)(volreq/Math.pow(2, n-1));
/*		System.out.println("vheck  "+(long)(volreq/Math.pow(2, n-1)));*/
		
		volreq=volreq%((int)Math.pow(2, n-1));
		
		
/*		System.out.println("volreq  "+volreq +" price  "+totprice);*/
		int flag=0;
		for(int i=0;i<n;i++)
		{
			if(Math.pow(2, i)>volreq)
			{
				flag=i;
				break;
			}
		}
		/*System.out.println("flag "+flag);*/
		long tprice=0;
		long min=Integer.MAX_VALUE;
		for(int i=flag-1;i>=0;i--)
		{
			if(Math.pow(2, i)<=volreq) {
				tprice=tprice+price[i];
				
				/*System.out.println("here  "+tprice);*/
				volreq-=Math.pow(2, i);
			}
			
			else if(tprice+price[i]<min)
			{
				min=tprice+price[i];
			/*	System.out.println("min "+min);*/
			}
		
			
			if(volreq==0)
				break;
		}
		
	min=Math.min(min, tprice);
		/*System.out.println(min);
		System.out.println("flagg "+flag);
		System.out.println("p "+price[flag]);*/
		/*
			System.out.println((totprice+ Math.min(tprice, price[flag])));*/
			return(totprice+ Math.min(min, price[flag]));
		
	}
	
	public static void main(String[] args) {
		Scanner s=new Scanner(System.in);
		
		int n=s.nextInt();
		int volreq=s.nextInt();
		int[] price=new int[n];
		for(int i=0;i<n;i++) {
			price[i]=s.nextInt();
		}
		
		int[] vol=new int[n];
		
		for(int i=0;i<n;i++)
			vol[i]=(int)Math.pow(2, i);
		
		System.out.println(minPrice(volreq,n,price));
	}

}
//44981600785557577
//5 787787787
//123456789 234567890 345678901 456789012 987654321
