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.*;
import java.io.*;

import static java.lang.Math.*;

public class Hello2018C {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        StringBuilder sb = new StringBuilder();
        int n = sc.nextInt();
        long L = sc.nextLong();
        ArrayList<Bottle> nums = new ArrayList<Bottle>();
        long start = 1;
        for (int i = 0; i < n; i++) {
            nums.add(new Bottle(start, sc.nextLong()));
            start *= 2;
        }
        for (int i = n-2; i >= 0; i-- ) {
            // if a smaller size is strictly worse
            if (nums.get(i).cost >= nums.get(i+1).cost) {
                nums.remove(i);
            }
        }
        long expectedCost = nums.get(0).cost;
        long amount = nums.get(0).amount;
        for (int i = 1; i < nums.size(); i++) {
            while (amount < nums.get(i).amount) {
                amount *= 2;
                expectedCost *= 2;
            }
            if (nums.get(i).cost >= expectedCost) {
                nums.remove(i);
                i--;
            } else {
                expectedCost = nums.get(i).cost;
            }
        }
        int i = nums.size()-1;
        long remaining = L;
        long bestCost =  Long.MAX_VALUE;
        long toAdd = 0;
        while (i >= 0 && remaining > 0) {
            bestCost = Math.min(bestCost,(remaining / nums.get(i).amount) * nums.get(i).cost + ((remaining % nums.get(i).amount == 0) ? 0 : nums.get(i).cost) + toAdd);
            toAdd += (remaining / nums.get(i).amount) * nums.get(i).cost;
            remaining -= (remaining / nums.get(i).amount) * nums.get(i).amount;
            i--;
        }
        sb.append(bestCost);



        System.out.print(sb);
    }

    public static class Bottle {
        long cost;
        long amount;
        public Bottle(long amount, long cost) {
            this.amount = amount;
            this.cost = cost;
        }
    }


    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }

        public FastScanner() {
            this(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextInt();
            }
            return a;
        }

        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextLong();
            }
            return a;
        }
    }
}
