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.Arrays;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        solve();
    }

    private static void solve() throws IOException {
        int n = Reader.nextInt();
        int l = Reader.nextInt();
        long[][] prices = new long[n][2]; // 0: price, 1: liters
        for (int i = 0; i < n; i++) {
            prices[i][0] = Reader.nextLong();
            prices[i][1] = 1 << i;
        }

        Arrays.sort(prices, Main::compare);
        System.out.println(go(l, prices));
    }

    private static long go(long liter, long[][] prices) {
        if (liter <= 0) return 0;
        long[] lastprice = prices[0];
        int i = 0;
        long cost = Long.MAX_VALUE;
        while (i < prices.length) {
            if (lastprice[1] < liter && compare(prices[i], lastprice) == 1) break;

            if (prices[i][1] < liter) {
                long num = liter / prices[i][1];
                long remain = liter % prices[i][1];
                cost = Math.min(cost, prices[i][0] * num + go(remain, prices));
            } else {
                cost = Math.min(cost, prices[i][0] + go(liter - prices[i][1], prices));
            }
            lastprice = prices[i];
            i++;
        }
        return cost;
    }

    private static int compare(long[] i1, long[] i2) {
        long p1 = i1[0] * i2[1];
        long p2 = i2[0] * i1[1];
        if (p1 > p2) return 1;
        if (p1 < p2) return -1;
        if (i1[1] > i2[1]) return -1;
        if (i1[1] < i2[1]) return 1;
        return 0;
    }

    private static class Reader {
        static BufferedReader reader;
        static StringTokenizer tokenizer;

        /**
         * call this method to initialize reader for InputStream
         */
        static void init(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        /**
         * get next word
         */
        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
            return tokenizer.nextToken();
        }

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

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

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

}
