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.IOException;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.*;
import java.io.*;

public class Main {
    public class point {
        char x;
        double y;

        point(char a, double b) {
            x = a;
            y = b;
        }
    }

    long pow(long x, long y) {
        if (y == 0) return 1;
        long c = pow(x, y / 2);
        c = (c * c) % 1000000000;
        if (y % 2 == 1) {
            c *= x;
            c %= p111;
        }
        return c;
    }

    long p111;

    int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    boolean x = true;

    boolean dfs(int v) {
        if (q.get(v).size() == 0) return true;
        int y = 0;
        for (int i = 0; i < q.get(v).size(); i++) {
            if (dfs(q.get(v).get(i))) {
                y++;
            }
        }
        if (y < 3) {
            x = false;
        }
        return false;
    }

    ArrayList<ArrayList<Integer>> q;

    public void solve() throws IOException {
        int n = nextInt();
        int l = nextInt();
        long[] a = new long[31];
        Arrays.fill(a, (long) 1e18);
        a[0] = nextInt();
        long res1 = Long.MAX_VALUE;
        for (int i = 1; i < n; i++) {
            a[i] = Math.min(2 * a[i - 1], nextInt());
            if ((1 << i) >= l) {
                res1 = Math.min(res1, a[i]);
            }
        }
        long res = 0;
        for (int i = n - 1; i >= 0; i--) {
            long x = 1 << i;
            long y = l / x;
            res += y * a[i];
            l -= y * x;
            res1 = Math.min(res1,res + a[i]);
        }
        out.print(Math.min(res, res1));
    }

    StringTokenizer sc;
    BufferedReader br;
    PrintWriter out;

    Long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    String nextToken() throws IOException {
        while (sc == null || !sc.hasMoreTokens()) {
            try {
                sc = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return sc.nextToken();
    }

    public static void main(String[] args) throws IOException {
        try {
            Locale.setDefault(Locale.US);
            new Main().run();
        } catch (Exception e) {

        }
    }

    public Integer nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public void run() throws IOException {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            solve();
            out.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }
}