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.math.BigInteger;
import java.util.Scanner;

public class PartyLemonade {
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);

        BigInteger minimumCost = new BigInteger("4000000000000000000");
        int bottleType; //types of bottle available
        int lemonadeRequired; //required amount of lemonade

        bottleType = in.nextInt();
        lemonadeRequired = in.nextInt();
        int prices[] = new int[bottleType];

        for(int i=0; i<bottleType; i++) {
            prices[i] = in.nextInt();
        }

        for(int i=0; i<bottleType-1; i++) {
            if(prices[i+1] >= 2*prices[i]) { //if buying 2 of current bottle type is cheaper than buying one of the next type
                prices[i+1] = 2*prices[i];
            }
        }

        int currentBottleAmount;
        BigInteger tempBuyPrice = BigInteger.valueOf(0);
        BigInteger a, b; //temporary variable to do arithmetic operations with BigInteger
        for(int i=bottleType-1; i>=0; i--) {
            //amount of bottle needed (current iteration)
            currentBottleAmount = lemonadeRequired/(int)Math.pow(2, i);

            //current bottle amount * current bottle price
            a = new BigInteger(Integer.toString(currentBottleAmount));
            b = new BigInteger(Integer.toString(prices[i]));
            tempBuyPrice = tempBuyPrice.add(a.multiply(b));
            lemonadeRequired -= currentBottleAmount * (int)Math.pow(2, i);

            //finding minimum cost, comparing current minimum cost to (current bottle amount * current bottle price)
            a = new BigInteger(Integer.toString(lemonadeRequired>0 ? 1 : 0));
            b = new BigInteger(Integer.toString(prices[i]));
            b = tempBuyPrice.add(a.multiply(b));
            if(minimumCost.compareTo(b) == 1) { //if(minimumCost > b): (minimumCost is not minimum -> we replace minimumCost)
                minimumCost = b;
            }
        }
        System.out.println(minimumCost);
        in.close();
    }
}