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.ByteArrayInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.List;
import java.util.Map;
import java.util.Queue;
import java.util.Set;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.logging.Level;
import java.util.logging.Logger;

/**
 *
 * @author ssaxena36 :D
 *
 */
public class NewClass {

    void solve() {
        int n = inpi(), l = inpi();
        for (int i = 0; i < n; i++) {
            c[i] = inpl();
        }
        power[0] = 1;
        for (int i = 1; i <= 31; i++) {
            power[i] = power[i - 1] * 2L;
        }
        lm = (long) 1e18;
        for (int i = n - 2; i >= 0; i--) {
            c[i] = Math.min(c[i], c[i + 1]);
        }
        for (int i = 1; i < n; i++) {
            c[i] = Math.min(c[i], c[i - 1] * 2L);
        }
        for (int i = n; i < 32; i++) {
            c[i] = c[i - 1] * 2L;
        }
        for (int i = 30; i >= 0; i--) {
            if (power[i] > m) {
                lm = c[i];
            }
        }
        out.println(gen(30, l));
    }
    long n, m, r = 0, lm, inf = (long) 1e18;
    long c[] = new long[32], power[] = new long[33];

    long gen(int s, long t) {
        if (t <= 0) {
            return 0;
        }
        if (t >= power[s + 1]) {
            return inf;
        }
        if (s == 0) {
            return c[0];
        } else {
            return Math.min(c[s] + gen(s - 1, t - power[s]), gen(s - 1, t));
        }
    }
    class Point {

        int x;
        int y;

        Point(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }

    public boolean isPrime(long n) {
        return BigInteger.valueOf(n).isProbablePrime(5);
    }

    public boolean[] SieveOfEratosthenes(int n) {
        boolean prime[] = new boolean[n + 1];
        Arrays.fill(prime, true);
        for (int p = 2; p * p <= n; p++) {
            if (prime[p] == true) {
                for (int i = p * 2; i <= n; i += p) {
                    prime[i] = false;
                }
            }
        }
        for (int i = 2; i < n; i++) {
            if (prime[i]) {
                //do some stuff
            }
        }
        return prime;
    }
    InputStream obj;
    PrintWriter out;
    String check = "";
    int len;

    public static void main(String[] args) throws IOException {
        new Thread(null, new Runnable() {
            public void run() {
                try {
                    new NewClass().main1();
                } catch (IOException ex) {
                    Logger.getLogger(NewClass.class.getName()).log(Level.SEVERE, null, ex);
                }
            }
        }, "child-thread", 1 << 26).start();

    }

    void main1() throws IOException {
        out = new PrintWriter(System.out);
        obj = check.isEmpty() ? System.in : new ByteArrayInputStream(check.getBytes());
        //   obj=check.isEmpty() ? new FileInputStream("/home/ssaxena36/Desktop/file.in") : new ByteArrayInputStream(check.getBytes());
        solve();
        out.flush();
        out.close();
    }
    byte inbuffer[] = new byte[1024];
    int lenbuffer = 0, ptrbuffer = 0;

    int readByte() {
        if (lenbuffer == -1) {
            throw new InputMismatchException();
        }
        if (ptrbuffer >= lenbuffer) {
            ptrbuffer = 0;
            try {
                lenbuffer = obj.read(inbuffer);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        if (lenbuffer <= 0) {
            return -1;
        }
        return inbuffer[ptrbuffer++];
    }

    boolean isSpaceChar(int c) {
        return (!(c >= 33 && c <= 126));
    }

    int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b));
        return b;
    }

    String inps() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    int inpi() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    long inpl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    float inpf() {
        return Float.parseFloat(inps());
    }

    double inpd() {
        return Double.parseDouble(inps());
    }

    char inpc() {
        return (char) skip();
    }

    int[] inpia(int n) {
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = inpi();
        }
        return a;
    }

    long[] inpla(int n) {
        long a[] = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = inpl();
        }
        return a;
    }

    String[] inpsa(int n) {
        String a[] = new String[n];
        for (int i = 0; i < n; i++) {
            a[i] = inps();
        }
        return a;
    }

    double[][] inpdm(int n, int m) {
        double a[][] = new double[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                a[i][j] = inpd();
            }
        }
        return a;
    }

    int[][] inpim(int n, int m) {
        int a[][] = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                a[i][j] = inpi();
            }
        }
        return a;
    }
}
