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.
// package Mathematical;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class PartyLemonade {
    public static void main(String[] args)throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
//        long temp=(long)Math.pow(2,63);
//        System.out.println(temp);
        String line[]=br.readLine().split(" ");
        int n=Integer.parseInt(line[0]);
        int l=Integer.parseInt(line[1]);
        long cost[]=new long[32];
        long min_cost[]=new long[32];
        line=br.readLine().split(" ");
        for(int i=0;i<n;i++){
            cost[i]=Long.parseLong(line[i]);
        }
        for(int i=n;i<32;i++){
            cost[i]=Long.MAX_VALUE/2;
        }
//        System.out.println(cost[31]);
        min_cost[0]=cost[0];
        for(int i=1;i<32;i++){
            min_cost[i]=Math.min(cost[i],2*min_cost[i-1]);
//            System.out.print(min_cost[i]+" ");
        }
//        System.out.println();
        long ans=0;
        long ans2=Long.MAX_VALUE;
        long sum=0;
        for(int i=31;i>=0;i--){
            long temp=1<<i;
            if((temp&l)!=0){
//                System.out.println(i);
                ans+=min_cost[i];
//                System.out.println(ans+" ");
            }
            else{
               ans2=Math.min(ans2,min_cost[i]+ans);
            }
        }
        System.out.println(Math.min(ans,ans2));
    }
}
