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.File;
import java.util.Scanner;
import java.util.StringTokenizer;

public class p036 {
	public static void main(String args[]) throws Exception {
		StringTokenizer stok = new StringTokenizer(new Scanner(System.in).useDelimiter("\\A").next());
		StringBuilder sb = new StringBuilder();
		int n = Integer.parseInt(stok.nextToken());
		long L = Long.parseLong(stok.nextToken());
		long[] a = new long[32];
		for (int i = 0; i < n; i++) {
			a[i] = Long.parseLong(stok.nextToken());
		}
		for(int i=n;i<32;i++) a[i] = Long.MAX_VALUE;
		for(int i=0;i<32;i++) {
			long f=1;
			for(int j=i+1;j<32;j++) {
				f*=2;
				a[j] = Math.min(a[j], a[i]*f);
			}
		}
		long[] b = new long[32];
		int i=0;
		while(L>0) {
			b[i++]=L%2;
			L/=2;
		}
		long tot = 0,min = Long.MAX_VALUE;
		for(i=31;i>=0;i--) {
			if(b[i]==1) tot += a[i];
			else min = Math.min(min, tot+a[i]);
		}
		min = Math.min(tot, min);
		System.out.println(min);
	}
}