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 Main
{
    //yun bheegi bheegi si barsaat bhi h.....
   
	static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

	static ArrayList<Integer> primes = new ArrayList<Integer>();
	static int limit = 1000000007;

	public static void main (String[] args)
	{
		FastReader reader = new FastReader();
		int n=reader.nextInt();
		int l=reader.nextInt();
		long c[]=new long[31];
		Arrays.fill(c, Integer.MAX_VALUE);
		for( int i=0;i<n;i++)
		{
		    long x=reader.nextLong();
		    if(i==0)
		    c[i]=x;
		    else
		    c[i]=Math.min(x, 2*c[i-1]);
		}
		for( int i=n;i<=30;i++)
		{
		    c[i]= 2*c[i-1];
		}
		long ans=0;
		long ans1=Long.MAX_VALUE;
		for( int i=30;i>=0;i--)
		{
		    if((l&(1<<i))==(1<<i))
		    ans+=c[i];
		    else
		    {
		       long sup=ans+c[i];
		       ans1=Math.min(sup, ans1);
		    }
		}
		System.out.println(Math.min(ans1, ans));
		
	}

	static void sieveOfEratosthenes(int n)
	{
			// Create a boolean array "prime[0..n]" and initialize
			// all entries it as true. A value in prime[i] will
			// finally be false if i is Not a prime, else true.
			boolean[] prime = new boolean[n+1];
			for(int i=0;i<n;i++)
					prime[i] = true;

			for(int p = 2; p*p <=n; p++)
			{
					// If prime[p] is not changed, then it is a prime
					if(prime[p] == true)
					{
							// Update all multiples of p
							for(int i = p*2; i <= n; i += p)
									prime[i] = false;
					}
			}

			// Print all prime numbers
			for(int i = 2; i <= n; i++)
			{
					if(prime[i] == true)
							primes.add (i);
			}
	}
}

class Pair{
    int size;
    int l;
    int r;
    Pair( int size, int l, int r)
    {
        this.size=size;
        this.l=l;
        this.r=r;
    }
}
class myComparator implements Comparator<Pair>
{
    public int compare( Pair a, Pair b)
    {
     if(a.size==b.size)
     {
         return Integer.compare(a.l,b.l);
     }else
     return Integer.compare(b.size,a.size);
    }
}