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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author triveni
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskC {
		long inf = (long) 1e18 + 7;
		long[] lemonades = new long[32];

		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int n = in.nextInt();
			int L = in.nextInt();
			for (int i = 0; i < 32; ++i) lemonades[i] = inf;
			for (int i = 0; i < n; ++i) {
				lemonades[i] = in.nextInt();
			}
			for (int i = 1; i < 32; ++i) {
				if (lemonades[i - 1] * 2 < lemonades[i]) lemonades[i] = 2 * lemonades[i - 1];
			}
			long ans = solve(L);
			out.println(ans);
		}

		boolean isSet(int n, int idx) {
			return (n & (1 << idx)) != 0;
		}

		long solve(int L) {
			if (L == 0) return 0;
			int i = 30;
			for (; i >= 0; --i) if (isSet(L, i)) break;
			long ans = inf;
			for (int j = 31; j > i; --j) ans = Math.min(ans, lemonades[j]);
			long ans1 = solve(L ^ (1 << i)) + lemonades[i];
			return Math.min(ans, ans1);
		}

	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream inputStream) {
			reader = new BufferedReader(new InputStreamReader(inputStream));
			tokenizer = null;
		}

		public InputReader(String inputFile) throws FileNotFoundException {
			reader = new BufferedReader(new FileReader(inputFile));
			tokenizer = null;
		}

		public String nextLine() {
			String curr = "";
			try {
				curr = reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
			return curr;
		}

		public String nextString() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(nextLine());
				} catch (Exception e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextString());
		}

	}
}

