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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main
{
    static long c[] ;   static int n ;

    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                solve();
            }
        }, "1", 1 << 26).start();
    }
    static void solve () {
        FastReader fr =new FastReader();    PrintWriter op =new PrintWriter(System.out);
        n =fr.nextInt() ;   int l =fr.nextInt() ,i ;   c =new long[n+1] ;
        for (i =1 ; i<=n ; ++i) c[i] =fr.nextLong() ;

        op.println(solve(l)) ;  op.flush();    op.close();
    }
    static long solve (int l) {
        int i ,j ,k ,m ;    long cst =Long.MAX_VALUE ,cost ;

        j =(int)Math.ceil(Math.log10(l)/Math.log10(2.0))+1 ;
        for (i =j ; i<=n ; ++i)  cst =Math.min(cst , c[i]) ;//1 choice is c[j]
        
        if (j>1) {
            k =Math.min(j-2 , n-1) ;//0-k;powers of 2 possible
            double dm ,min =1e9+1.0 ;   m =-1 ;
            for (i =0 ; i<=k ; ++i) {
                dm =c[i+1]/(double)(1<<i) ;
                if (dm<min) {
                    min =dm ;   m =i ;
                }
            }
            i =l/(1<<m) ;   cost =c[m+1]*(long)i ;   l %= (1<<m) ;
            if (l>0)    cost += solve (l) ;
            cst =Math.min(cost,cst) ;
        }
        return cst ;
    }
    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();
        }

        String nextLine() {
            String str ="";

            try
            {
                str =br.readLine();
            }
            catch(IOException e)
            {
                e.printStackTrace();
            }

            return str;
        }

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

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