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.
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    public class Obj implements Comparable<Obj>{
        public int a;
        public int b;
        
        public Obj(int a_, int b_){
            a = a_;
            b = b_;
        }
        
        public int compareTo(Obj other){
            if (a != other.a){
                return a - other.a;
            }else{
                return b - other.b;
            }
        }
        
    }
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
        Codechef cf = new Codechef();
        cf.Solve();
	}
	
	
	public void Solve(){
        MyScanner sc = new MyScanner();
        int n = sc.nextInt();
        long L = sc.nextLong();
        long[] val = new long[n];
        long[] cost = new long[n];
        long z = 1L;
        for (int i = 0; i < n; ++i){
            cost[i] = sc.nextLong();
            val[i] = z;
            z *= 2L;
        }
        long[] dp = new long[n];
        dp[0] = cost[0];
        for (int i = 1; i < n; ++i){
            long k = dp[i-1]  * 2;
            if (cost[i] < k){
                dp[i] = cost[i];
            }else{
                dp[i] = k;
            }
        }
        long best = recur(L, val, dp, n);
        System.out.println(best);
	}
	
	public long recur(long cur, long[] val, long[] cost, int n){
	    if (cur <= 0L) return 0;
	    long best = cost[0] * cur;
	    int idx = 0;
	    for (int i = 0; i < n; ++i){
	        if (val[i] <= cur){
	            idx = i;
	        }
	        long k = cur / val[i];
	        if (cur % val[i] != 0) k++;
	        long need = k * cost[i];
	        best = Math.min(best, need);
	    }
	    
	    long k = cur / val[idx];
	    long rem = cur - k * val[idx];
	    long c = k * cost[idx];
	    c += recur(rem, val, cost, n);
	    best = Math.min(best, c);
	    
	    return best;
	}

	//-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         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;
      }

   }
}
