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.*;
import java.util.*;

public class Mainn {

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

		public InputReader() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

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

		public long nextLong() {
			return Long.parseLong(next());
		}
	}

	public static void main(String[] args) {

		// InputStream inputStream = System.in; // Useful when taking input other than
		// console eg file handling // check ctor of inputReader
		InputReader scn = new InputReader();

		int n = scn.nextInt(), l = scn.nextInt();
		long[] arr = new long[n + 1];
		for (int i = 1; i <= n; i++) {
			arr[i] = scn.nextInt();
		}
long xxx = System.currentTimeMillis();
		long[] cost = new long[32];
		Arrays.fill(cost, Long.MAX_VALUE);
		cost[0] = 0;
		cost[1] = arr[1];
		for (int i = 1; i <= n; i++) {
			for (int j = i + 1; j <= n; j++) {
				long div = (long) Math.pow(2, j - i);
				cost[j] = Math.min(cost[j], Math.min(div * arr[i], arr[j]));
			}
		}

		for (int i = 1; i <= n; i++) {
			for (int j = i + 1; j <= 31; j++) {
				long div = (long) Math.pow(2, j - i);
				cost[j] = Math.min(cost[j], div * arr[i]);
			}
		}

		long ans = Long.MAX_VALUE;

		for (int i = 31; i > 0; i--) {
			long lit = (long) Math.pow(2, i - 1);
			long t = cost[i];
			long ll = (long) Math.pow(2, i - 1);
			long tot = (l - lit) / ll + 1;
			if ((l - lit) % ll == 0) {
				tot--;
			}
			if (lit < l) {
				lit += tot * (long) Math.pow(2, i - 1);
				t += tot * cost[i];
			}

			if (t < ans) {
				ans = t;
			}

			lit -= (long) Math.pow(2, i - 1);
			t -= cost[i];

			for (int j = i - 1; j > 0; j--) {
				long lll = (long) Math.pow(2, j - 1);
				long tott = (l - lit) / lll + 1;
				if ((l - lit) % lll == 0) {
					tott--;
				}
				if (lit < l) {
					lit += tott * (long) Math.pow(2, j - 1);
					t += tott * cost[j];
				}
				if (t < ans) {
					ans = t;
				}

				lit -= (long) Math.pow(2, j - 1);
				t -= cost[j];
			}

		}

		System.out.println(ans);
	}
}