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.io.*;
import java.util.Arrays;
import java.util.StringTokenizer;

public class C {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        int n = in.nextInt();
        int l = in.nextInt();
        long[] v = new long[32];
        for (int i = 0; i < 32; ++i) {
            v[i] = Long.MAX_VALUE;
        }
        for (int i = 0; i < n; ++i) {
            v[i] = in.nextLong();
        }
        for (int i = 0; i < 31; ++i) {
            if (v[i] * 2 < v[i + 1]) {
                v[i + 1] = v[i] * 2;
            }
        }
        String b = Integer.toBinaryString(l);
        int length = b.length();
        long sum = 0;
        for (int i = b.length() - 1, index = 0; index < 32; --i, ++index) {
            if (v[index] < sum) sum = v[index];
            char s = i <0 ? '0' : b.charAt(i);
            if (s == '1') sum += v[index];
        }
        out.print(sum);
        out.close();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return tokenizer.nextToken();
        }

        public String nextLine() {
            String ret = null;
            try {
                ret = reader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return ret;
        }

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

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

        public float nextFloat() {
            return Float.parseFloat(next());
        }

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