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.*;
import java.text.*;
import java.math.*;
public class Main{
    static final long MOD = (long)1e9+7;
    static FastReader in;
    static long[][] C;
    static HashMap<Long, Long> map;
    public static void main(String[] args){
        in = new FastReader();
        int N = ni();
        long L = nl();
        C = new long[N][2];
        for(int i = 0; i< N; i++)C[i] = new long[]{1l<<i, nl()};
        map = new HashMap<>();
        pn(calc(N-1,L));
    }
    
    static long calc(int idx, long rem){
        if(rem<=0)return 0;
        if(idx==0){
            return ((rem+C[0][0]-1)/C[0][0])*C[0][1];
        }else{
            long cur = Long.MAX_VALUE;
            long x = get(idx, rem);
            if(map.containsKey(x))return map.get(x);
            if(rem<=C[idx][0])return Math.min(C[idx][1], calc(idx-1, rem));
            else{
                long c1 = (rem+C[idx][0]-1)/C[idx][0], c2 = rem/C[idx][0];
                cur = Math.min(cur, c1*C[idx][1]);
                cur = Math.min(cur, c2*C[idx][1] + calc(idx-1, rem- c2*C[idx][0]));
                cur = Math.min(cur, calc(idx-1, rem));
            }
            map.put(x, cur);
            return cur;
        }
    }
    
    static long get(long idx, long rem){
        return idx*(long)1e10+rem;
    }
    
    static void p(Object o){
        System.out.print(o);
    }
    
    static void pn(Object o){
        System.out.println(o);
    }
    
    static String n(){
        return in.next();
    }
    
    static String nln(){
        return in.nextLine();
    }
    
    static int ni(){
        return Integer.parseInt(in.next());
    }
    
    static int[] ia(int N){
        int[] a = new int[N];
        for(int i = 0; i<N; i++)a[i] = ni();
        return a;
    }
    
    static long[] la(int N){
        long[] a = new long[N];
        for(int i = 0; i<N; i++)a[i] = nl();
        return a;
    }
    
    static long nl(){
        return Long.parseLong(in.next());
    }
    
    static double nd(){
        return Double.parseDouble(in.next());
    }
    
    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;
        }
    }
} 