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.*;

 
 
import java.util.*;
/*
 
 
 */


 
 
 
 
public class C {
    static FastReader sc=null;
    
	
	public static void main(String[] args) {
		sc=new FastReader();
		int n=sc.nextInt(),l=sc.nextInt();
		int c[]=sc.readArray(n);
		//MIN COST TO PURCHASE EACH OF THEM IS FOUND
		for(int i=0;i+1<n;i++)c[i+1]=Math.min(c[i+1], 2*c[i]);
		long cost=Long.MAX_VALUE;
		long left=l;
		long currVal=0;
		for(int i=n-1;i>=0 && left>0;i--) {
			//if we pick all from it 
			long val=(left/(1<<i))*(c[i]);
			currVal+=val;
			left=left%(1<<i);
			if(left!=0)cost=Math.min(cost, currVal+c[i]);
			else cost=Math.min(cost, currVal);
		}
		System.out.println(cost);
		
		
		
		
		

		
	}
	
    
    
    
    static void ruffleSort(int a[]) {
    	ArrayList<Integer> al=new ArrayList<>();
    	for(int i:a)al.add(i);
    	Collections.sort(al);
    	for(int i=0;i<a.length;i++)a[i]=al.get(i);
    }
    
    static void ruffleSort(long a[]) {
        ArrayList<Long> al=new ArrayList<>();
        for(long i:a)al.add(i);
        Collections.sort(al);
        for(int i=0;i<a.length;i++)a[i]=al.get(i);
    }
    
    static int[] reverse(int a[]) {
        ArrayList<Integer> al=new ArrayList<>();
        for(int i:a)al.add(i);
        Collections.sort(al,Collections.reverseOrder());
        for(int i=0;i<a.length;i++)a[i]=al.get(i);
        return a;
    }
 
    static int gcd(int a,int b) {
		if(b==0)return a;
		else return gcd(b,a%b);
	}  
    static long gcd(long a,long b) {
		if(b==0)return a;
		else return gcd(b,a%b);
	}  
        
 
    
    
    
    static void print(long a[]) {
        for(long e:a) {
            System.out.print(e+" ");
        }
        System.out.println();
    }
    static void print(char a[]) {
        for(char e:a) {
            System.out.print(e);
        }
        System.out.println();
    }
    
    
    static void print(int a[]) {
        for(int e:a) {
            System.out.print(e+" ");
        }
        System.out.println();
    }
    
    
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
        int[] readArray(int n) {
            int a[]=new int [n];
            for(int i=0;i<n;i++) {
                a[i]=sc.nextInt();
            }
            return a;
        }
        long[] readArrayL(int n) {
            long a[]=new long [n];
            for(int i=0;i<n;i++) {
                a[i]=sc.nextLong();
            }
            return a;
        }
    } 
}