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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Objects;
import java.util.Scanner;

public class Codeforces913C {

    private static class Pair implements Comparable {

        Long volumes;
        Double unitPrice;
        Long price;

        public Pair(Long volumes, Double unitPrice, Long price) {
            this.volumes = volumes;
            this.unitPrice = unitPrice;
            this.price = price;
        }

        public Long getVolumes() {
            return volumes;
        }

        public void setVolumes(Long volumes) {
            this.volumes = volumes;
        }

        public Double getUnitPrice() {
            return unitPrice;
        }

        public void setUnitPrice(Double unitPrice) {
            this.unitPrice = unitPrice;
        }

        public Long getPrice() {
            return price;
        }

        public void setPrice(Long price) {
            this.price = price;
        }

        @Override
        public int compareTo(Object o) {
            return this.unitPrice.compareTo(((Pair) o).unitPrice);
        }

        @Override
        public String toString() {
            return "Pair{" + "volumes=" + volumes + ", unitPrice=" + unitPrice + ", price=" + price + '}';
        }

    }
    public static List<Pair> bottles;

    public static Long check(Long L, int start) {
        if (start < bottles.size() && L > 0) {
            Pair curPair = bottles.get(start);
//            System.out.println(L + " " + curPair.toString());
            Long numberOfBottles = L / curPair.getVolumes();
            L -= numberOfBottles * curPair.getVolumes();
            return numberOfBottles * curPair.getPrice() + Math.min(curPair.getPrice(), check(L, start + 1));
        } else {
            return (long) 0;
        }
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        Integer n = scanner.nextInt();
        Long L = scanner.nextLong();
        Long roubles = new Long(0);
        scanner.nextLine();
        bottles = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            Long price = scanner.nextLong();
            Long volume = (long) Math.pow(2, i);
            Double unitPrice = (new Double(price)) / volume;
            bottles.add(new Pair(volume, unitPrice, price));
        }
        Collections.sort(bottles);
//        System.out.println(bottles);
//        while (L > 0) {
//            int index = check(L);
//            Pair curPair = bottles.get(index);
//            if(L>bottles.get(index).volumes){
//                
//                Long numberOfBottles = L/(curPair.volumes);
//                L-=numberOfBottles*bottles.get(index).getVolumes();
//                roubles+=numberOfBottles*bottles.get(index).price;
//            } else {
//                L-=bottles.get(index).getVolumes();
//                roubles+=bottles.get(index).price;
//            }
//        }
        System.out.println(check(L, 0));
    }
}
