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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class C {
	private static String[] costs;
	private static Double[] costsPerLiters;
	private static List<Integer> bottleTypes;

	public static void main(String[] args) {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		try {
			String[] data = br.readLine().split(" ");
			Integer n = Integer.parseInt(data[0]);
			Integer l = Integer.parseInt(data[1]);
			costs = br.readLine().split(" ");
			costsPerLiters = new Double[n];
			bottleTypes = new ArrayList<Integer>();
			
			for (int i = 0; i < n; i++) {
				bottleTypes.add(i + 1);
				costsPerLiters[i] = Integer.parseInt(costs[i]) / Math.pow(2, i);
			}
			
			bottleTypes.sort(new Comparator<Integer>() {
				@Override
				public int compare(Integer o1, Integer o2) {
					return Double.valueOf(costsPerLiters[o1 - 1]).compareTo(costsPerLiters[o2 - 1]);
				}
			});
			
			System.out.println(solve(l, 0, 0));
			
		} catch (NumberFormatException e) {
			e.printStackTrace();
		} catch (IOException e) {
			e.printStackTrace();
		}
		
	}
	
	private static long solve(long remainingLiters, int startTypeIdx, long cost) {
		
		
		if (remainingLiters > 0) {
			
			double liters = Math.pow(2, bottleTypes.get(startTypeIdx) - 1);
			if(liters > remainingLiters) {
				return Math.min(cost + Long.parseLong(costs[bottleTypes.get(startTypeIdx) - 1]), solve(remainingLiters, startTypeIdx + 1, cost));
			} else {
				return solve((long) (remainingLiters - (long) (remainingLiters/liters) * liters), startTypeIdx, (long) (cost + ((long) (remainingLiters/liters)) * Long.parseLong(costs[bottleTypes.get(startTypeIdx) - 1])));
			}
		}
		
		return cost;
		

	}
}


