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.util.Scanner;

public class code913C {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int m = sc.nextInt();
		int ppp = sc.nextInt();
		
		if(m==1){
			long p = sc.nextInt();
			System.out.println(p*ppp);
			return;
		}
		
		String pb = Integer.toBinaryString(ppp);
		char[] pc = pb.toCharArray();
		long[] price = new long[m];
		long[] money = new long[32];
		
		money[0] = Long.MAX_VALUE;
		for (int i = 0; i < m; i++) {
			price[i] = sc.nextInt();
			money[0] = Long.min(money[0], price[i]);
		}
		
		sc.close();
		
		for(int i = 1; i < pc.length + 1; i++){
			long min = Long.MAX_VALUE;
			for(int j = i; j < m; j++){
				min = Long.min(min, price[j]);
			}
			money[i] = Long.min(money[i-1]*2, min);
		}
		
		long result = 0;
		for(int i = pc.length-1,j = 0;i>-1;i--){
			if(pc[i]=='1'){
				result += money[j];
				result = Long.min(result, money[j+1]);
			}
			j++;
		}
		
		System.out.println(result);
	}
}
