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{

	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 boolean[] used;

    static long func(long k, long[] arr, double[] wt){

        if(k==0){
            return Long.MAX_VALUE;
        }

        int mini=0;
        double min = Double.MAX_VALUE;
        
        for(int i=0;i<arr.length;i++){
            if(!used[i] && wt[i]<min){
                min = wt[i];
                mini = i;
            }
        }

        long qnt = (long)Math.pow(2, mini);
        
        if(k%qnt==0){
        
            long cur = k/qnt;
            k -= (cur*qnt);
            return (cur*arr[mini]);
        
        }else{
            used[mini] = true;
            long cur = k/qnt;
            k -= (cur*qnt);
            long res = (cur*arr[mini]);

            return res+Math.min( func(k, arr, wt), arr[mini] );
        }

    }

	public static void main(String[] args){
		FastReader sc = new FastReader();
		
        int n = sc.nextInt();
        long k = sc.nextLong();
        long[] arr = new long[n];
        double[] wt = new double[n];
        used = new boolean[n];

        for(int i=0;i<n;i++){
            long pow = (long)Math.pow(2, i);
            arr[i] = sc.nextLong();
            wt[i] = ((1.0*arr[i])/(1.0*pow));
        }

        long res = 0 ;
            
        System.out.println( func(k, arr, wt) );
	}
}