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.*;
import java.text.ParseException;
import java.util.*;


public class Codeforces  {

    
    
    public static void main(String[] args) throws IOException, ParseException{
        Kattio sc = new Kattio(System.in,System.out);
        //Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long l = sc.nextLong();
        ls = new long[32];
        for(int i=0 ; i<n ; i++){
            ls[i] = sc.nextLong();
            if(i>0){
                ls[i] = Math.min(ls[i],2*ls[i-1]);
            }
        }
        
        for(int i=n ; i<=31 ; i++){
            ls[i] =  ls[i-1]*2;
        }
        
        System.out.println(solution(l,31));
        
        
    }
    
    static long[] ls;
    
    private static long solution(long l, int ind) {
        if(l<=0){
            return 0;
        }
        long x = 1L<<ind;
        if(x<=l){
            return ls[ind] + solution(l-x,ind-1);
        }
        else{
            return Math.min(solution(l,ind-1),ls[ind]);
        }
    }

  
    static class couple {
        long a;
        long b;
        int prev = -1;
        couple(long a, long b){
            this.a =a;
            this.b =b;
        }
    }
    
    
    
    
    static class Kattio extends PrintWriter {
        public Kattio(InputStream i) {
            super(new BufferedOutputStream(System.out));
            r = new BufferedReader(new InputStreamReader(i));
        }
        public Kattio(InputStream i, OutputStream o) {
            super(new BufferedOutputStream(o));
            r = new BufferedReader(new InputStreamReader(i));
        }
        
        public Kattio(FileInputStream i) {
            super(new BufferedOutputStream(System.out));
            r = new BufferedReader(new InputStreamReader(i));
        }
        public Kattio(FileInputStream i, OutputStream o) {
            super(new BufferedOutputStream(o));
            r = new BufferedReader(new InputStreamReader(i));
        }
    public boolean hasMoreTokens() {
        return peekToken() != null;
    }

    public int nextInt() {
        return Integer.parseInt(nextToken());
    }

    public double nextDouble() {
        return Double.parseDouble(nextToken());
    }

    public long nextLong() {
        return Long.parseLong(nextToken());
    }

    public String next() {
        return nextToken();
    }



    private BufferedReader r;
    private String line;
    private StringTokenizer st;
    private String token;

    private String peekToken() {
        if (token == null)
            try {
                while (st == null || !st.hasMoreTokens()) {
                    line = r.readLine();
                    if (line == null) return null;
                    st = new StringTokenizer(line);
                }
                token = st.nextToken();
            } catch (IOException e) { }
        return token;
    }

    private String nextToken() {
        String ans = peekToken();
        token = null;
        return ans;
    }
}
    
}