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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;
import java.util.StringTokenizer;

public class c {
	static int N = 31;
	public static void main(String[] args) throws IOException {
		FastScanner in = new FastScanner(System.in);
		int n = in.nextInt();
		long L = in.nextInt();
		long[] cs = new long[N];
		Arrays.fill(cs, Long.MAX_VALUE);
		for(int i=0;i<n;i++)
			cs[i] = in.nextInt();
		for(int i=1;i<N;i++)
			cs[i] = Math.min(cs[i], cs[i-1]*2);
		for(int i=N-2;i>=0;i--)
			cs[i] = Math.min(cs[i], cs[i+1]);
		long ans, sum = 0;
		for(int i=0;i<N;i++)
			if((L & (1L << i)) != 0)
				sum += cs[i];
		ans = sum;
		for(int i=0;i<N;i++)
			if((L & (1L << i)) != 0)
				sum -= cs[i];
			else
				ans = Math.min(ans, sum + cs[i]);
		System.out.println(ans);
	}
	static class FastScanner {
	    BufferedReader br;
	    StringTokenizer st;
	    public FastScanner(InputStream i) {
	        br = new BufferedReader(new InputStreamReader(i));
	        st = new StringTokenizer("");
	    }
	    public String next() throws IOException {
	        if(st.hasMoreTokens())
	            return st.nextToken();
	        else
	            st = new StringTokenizer(br.readLine());
	        return next();
	    }
	    public int nextInt() throws IOException {
	        return Integer.parseInt(next());
	    }
	    public long nextLong() throws IOException {
	        return Long.parseLong(next());
	    }
	    public double nextDouble() throws IOException {
	        return Double.parseDouble(next());
	    }
	}
}
