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.
// not correct... somehow

import java.util.*;
import java.io.*;

public class PartyLemonade {
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		StringTokenizer t = new StringTokenizer(in.readLine());
		int N = Integer.parseInt(t.nextToken());
		int L = Integer.parseInt(t.nextToken());
		long[] cost = new long[32];
		t = new StringTokenizer(in.readLine());
		for(int i = 0; i < N; ++i)
			cost[i] = Long.parseLong(t.nextToken());
		for(int i = 1; i < N; ++i)
			cost[i] = Math.min(cost[i], cost[i - 1] << 1);
		for(int i = N; i < 32; ++i)
			cost[i] = cost[i - 1] << 1;
		long ans = cost[31];
		long last = 0;
		for(int i = 30; i >= 0; --i) {
			if(L >= 1 << i) {
				L -= 1 << i;
				last = last + cost[i];
			}
			if(L == 0)
				ans = Math.min(ans, last);
			else
				ans = Math.min(ans, last + cost[i]);
		}
		out.println(Math.min(last, ans));
		in.close();
		out.close();
	}
}