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 org.omg.CORBA.INTERNAL;
import sun.reflect.generics.tree.Tree;

import javax.print.DocFlavor;
import java.io.*;
import java.util.*;

import static java.lang.Integer.divideUnsigned;
import static java.lang.Integer.max;
import static java.lang.Long.min;
import static java.lang.Integer.min;
import static java.lang.Math.*;

public class Main {


    int n;
    int INF = (int) 1e9;
    long LNF = (long) (9 * 1e18);
    int mod = (int) (1e9 + 7);
    ArrayList<Integer> g[];
    int d[];

    public void solve() throws IOException {
//        pw.print(LNF);
        n = nextInt();
        int l = nextInt();
        long d[] = new long[32];
        Arrays.fill(d, LNF);
        for (int i = 0; i < n; i++) {
            d[i] = nextInt();
        }
        for (int i = 1; i <= 31; i++) {
            d[i] = min(d[i], d[i - 1] * 2);
        }
        for (int i = 30; i >= 0; i--) {
            d[i] = min(d[i], d[i + 1]);
        }
        long s = 0;
        long ans = LNF;
        for (int i = 30; i >= 0; i--) {
            if (l >= (1 << i)) {
                s += d[i];
                l -= (1 << i);
            }
            if (l < 1 << i) {
                ans = min(ans, s + d[i]);
            }
        }
        ans = min(ans, s);
        pw.print(ans);
    }

    int dfs(int v) {
        if (g[v].size() == 0) return 1;
        int ans = 0;
        for (int i = 0; i < g[v].size(); i++) {
            ans += dfs(g[v].get(i));
        }
        if (ans < 3) {
            pw.print("No");
            pw.close();
            System.exit(0);
        }
        return 0;
    }

    class road {
        int to;
        int w;

        public road(int t, int ww) {
            to = t;
            w = ww;
        }
    }

    class pair implements Comparable<pair> {
        int a, b;

        public pair(int aa, int bb) {
            a = aa;
            b = bb;
        }

        @Override
        public int compareTo(pair o) {
            if (a != o.a) return a - o.a;
            else return b - o.b;
        }
    }

    public void run() {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
//            br = new BufferedReader(new FileReader("input.txt"));
            pw = new PrintWriter(new OutputStreamWriter(System.out));
//            pw = new PrintWriter(new FileWriter("output.txt"));
            solve();
            pw.close();
        } catch (IOException e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    BufferedReader br;
    StringTokenizer in;
    PrintWriter pw;


    public String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

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

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

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