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.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;

public class Main {

    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

        String[] line = in.readLine().split(" ");
        int n = Integer.parseInt(line[0]);
        int L = Integer.parseInt(line[1]);

        line = in.readLine().split(" ");
        int[] C = new int[n];
        boolean[] can = new boolean[n];
        for (int i=0; i<n; ++i) {
            C[i] = Integer.parseInt(line[i]);
            boolean ok = true;
            for (int j=0; j<i; ++j) {
                if (((long)C[j] * (1<<(i-j))) <= C[i]) {
                    ok = false;
                }
            }
            can[i] = ok;
        }

        long ans = Long.MAX_VALUE;
        for (int i=0; i<n; ++i) {
            if (can[i]) { //i is the minimum limit
                long total = L;
                long cost = 0;
                for (int j=n-1; j>i; --j) {
                    if (can[j]) {
                        long count = total / (1<<j);
                        cost += count * C[j];
                        total %= (1<<j);
                    }
                }
                if (total > 0) {
                    long count = total / (1<<i);
                    if (total % (1<<i) != 0) {++count;}
                    cost += count * C[i];
                }
                ans = Math.min(ans, cost);
            }
        }

        out.write(ans + "\n");
        in.close();
        out.close();
    }
}
