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.*;

public class Test {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        long L = sc.nextLong();
        long arr[] = new long[32];
        for(int i=0;i<32;i++){
            arr[i] = Long.MAX_VALUE;
        }
        for(int i=0;i<n;i++){
            arr[i] = sc.nextLong();
        }
        for(int i =1;i<=31;i++){
            if((arr[i-1]*2)<arr[i])
                    arr[i] = 2*arr[i-1];
        }
        String str = Long.toBinaryString(L);
        StringBuilder str1 = new StringBuilder(str);
        str = str1.reverse().toString();
        int len = str.length();
        long sum_so_far = 0;
        for(int i = 0;i<len;i++){
           if(arr[i]<=sum_so_far)
                sum_so_far=arr[i];
           if(str.charAt(i)=='1')
               sum_so_far+=arr[i];
        }
        for(int i = len;i<31;i++){
           if(arr[i]<=sum_so_far)
                sum_so_far=arr[i];
        }
        System.out.println(sum_so_far);
    }
}
