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;

public class C {

	static int arr[],n;
	static long min[];
	static boolean isPowerOfTwo(long x) {

		return x != 0 && ((x & (x - 1)) == 0);

	}

	static long count(long l)
	{
		if(l==0)
		{
			return 0 ;
		}
		int x = (int) (Math.ceil(Math.log(l) / Math.log(2) * 1.0));
		//System.out.println("L "+l+" X "+x);
		if(x>=n)
		{
			long k = (long)(Math.pow(2, n-1));
			//System.out.println("l/k = "+(int)(l/k)+" l%k="+l%k+" minna "+min[n-1]);
			
			return (long)(l*1.0/k*1.0)*(long)min[n-1] + (long)count(l%k);
		}
		if (isPowerOfTwo(l)) {
			return(min[x]);
		} else {
			
				int k = (int)(Math.pow(2, x-1));
				return Math.min(min[x],(long)min[x-1] + (long)count(l - k));
		}
	}
	public static void main(String args[]) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int l;
		String str[] = br.readLine().split(" ");
		n = Integer.parseInt(str[0]);
		l = Integer.parseInt(str[1]);

		arr = new int[n];
		str = br.readLine().split(" ");
		for (int i = 0; i < n; i++) {
			arr[i] = Integer.parseInt(str[i]);
		}

		min = new long[n];

		for (int i = 0; i < n; i++) {
			min[i] = arr[i];
			for (int j = 0; j < n; j++) {
				if (j >= i) {
					min[i] = Math.min(min[i], arr[j]);
				} else {
					min[i] = Math.min(min[i], min[j] * (int) (Math.pow(2, i - j)));
				}
			}
			 //System.out.println(min[i]);
		}
		System.out.println(count(l));
		

	}

}
