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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class CTask {

    public static void main(String[] args) throws IOException {
        MyInputReader in = new MyInputReader(System.in);
        int n = in.nextInt();
        long l = in.nextLong();
        long[] arr = new long[32];
        for (int i = 0; i < n; i++) {
            arr[i] = in.nextLong();
        }
        for (int i = 1; i < n; i++) {
            arr[i] = Math.min(arr[i], arr[i - 1] * 2);
        }
        //System.out.println(compute(n,  l, arr));
        long mn = Long.MAX_VALUE;
        for (long i = 0; i < 32; i++) {
            long cur = ((l >> i) | 1) << i;
            if (cur < l) {
                continue;
            }
            mn = Math.min(compute(n, cur, arr), mn);
        }
        System.out.println(mn);
    }

    static long compute(int n, long l, long[] arr) {
        long ans = 0;
        for (int i = n - 2; i >= 0; i--) {
            long m = (l >> i) & 1;
            if (m == 1) {
                ans += arr[i];
            }
        }
        ans += l / (1 << n - 1) * arr[n - 1];
        return ans;
    }

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

        public MyInputReader(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) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

    }

}