Problem: Pasha decided to invite his friends to a tea party. For that occasion, he has a large teapot with the capacity of w milliliters and 2n tea cups, each cup is for one of Pasha's friends. The i-th cup can hold at most ai milliliters of water.

It turned out that among Pasha's friends there are exactly n boys and exactly n girls and all of them are going to come to the tea party. To please everyone, Pasha decided to pour the water for the tea as follows:

  * Pasha can boil the teapot exactly once by pouring there at most w milliliters of water; 
  * Pasha pours the same amount of water to each girl; 
  * Pasha pours the same amount of water to each boy; 
  * if each girl gets x milliliters of water, then each boy gets 2x milliliters of water. 



In the other words, each boy should get two times more water than each girl does.

Pasha is very kind and polite, so he wants to maximize the total amount of the water that he pours to his friends. Your task is to help him and determine the optimum distribution of cups between Pasha's friends.

Input

The first line of the input contains two integers, n and w (1 ≤ n ≤ 105, 1 ≤ w ≤ 109) — the number of Pasha's friends that are boys (equal to the number of Pasha's friends that are girls) and the capacity of Pasha's teapot in milliliters.

The second line of the input contains the sequence of integers ai (1 ≤ ai ≤ 109, 1 ≤ i ≤ 2n) — the capacities of Pasha's tea cups in milliliters.

Output

Print a single real number — the maximum total amount of water in milliliters that Pasha can pour to his friends without violating the given conditions. Your answer will be considered correct if its absolute or relative error doesn't exceed 10 - 6.

Examples

Input

2 4
1 1 1 1


Output

3

Input

3 18
4 4 4 2 2 2


Output

18

Input

1 5
2 3


Output

4.5

Note

Pasha also has candies that he is going to give to girls but that is another task...

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;
 
    public  class Sample implements Runnable
    {
          
         

        public static void solve()
        { 
            
           int n=i();
           int p=i();
           int[] a=new int[2*n];
           for(int i=0;i<2*n;i++)a[i]=i();
           Arrays.sort(a);
           out.println(Math.min(Math.min(a[0],1.0*a[n]/2)*3.0*n,p));
           
          


        }

          public void run()
          {   
              solve();
              out.close();
          }

          public static void main(String[] args) throws IOException
          { 
                new Thread(null, new Sample(), "whatever", 1<<26).start();
          }
         static class Pair implements Comparator<Pair>
         {
            int a;
            int b;
            Pair(){}
            Pair(int a,int b)
            {
                       this.a=a;
                       this.b=b;
            }
   
            public int compare(Pair p1,Pair p2)
           {
                 return p2.b-p1.b;
           }
        }
        
       
         
    ////////////////////////////////////////////////////// Merge Sort ////////////////////////////////////////////////////////////////////////
     
   static class Merge 
   {

        public static void sort(long inputArr[]) 
        {
            int length = inputArr.length;
            doMergeSort(inputArr,0, length - 1);
        }

        private static void doMergeSort(long[] arr,int lowerIndex, int higherIndex) 
        {        
            if (lowerIndex < higherIndex) {
                int middle = lowerIndex + (higherIndex - lowerIndex) / 2;
                doMergeSort(arr,lowerIndex, middle);
                doMergeSort(arr,middle + 1, higherIndex);
                mergeParts(arr,lowerIndex, middle, higherIndex);
            }
        }

        private static void mergeParts(long[]array,int lowerIndex, int middle, int higherIndex) 
        {
            long[] temp=new long[higherIndex-lowerIndex+1];
            for (int i = lowerIndex; i <= higherIndex; i++) 
            {
                temp[i-lowerIndex] = array[i];
            }
            int i = lowerIndex;
            int j = middle + 1;
            int k = lowerIndex;
            while (i <= middle && j <= higherIndex) 
            {
                if (temp[i-lowerIndex] < temp[j-lowerIndex]) 
                {
                    array[k] = temp[i-lowerIndex];
                    i++;
                } else {
                    array[k] = temp[j-lowerIndex];
                    j++;
                }
                k++;
            }
            while (i <= middle) 
            {
                array[k] = temp[i-lowerIndex];
                k++;
                i++;
            }
            while(j<=higherIndex)
            {
                array[k]=temp[j-lowerIndex];
                k++;
                j++;
            }
        }

    }
        
      
    /////////////////////////////////////////////////////////// Methods ////////////////////////////////////////////////////////////////////////


     static boolean isPal(String s)
     {
        for(int i=0, j=s.length()-1;i<=j;i++,j--)
        {
                if(s.charAt(i)!=s.charAt(j)) return false;
        }
        return true;
     }
     static String rev(String s)
     {
                StringBuilder sb=new StringBuilder(s);
                sb.reverse();
                return sb.toString();
     }
     static int gcd(int a,int b){return (a==0)?b:gcd(b%a,a);}
     static long gcdExtended(long a,long b,long[] x)
     {

        if(a==0){
            x[0]=0;
            x[1]=1;
            return b;
        }
        long[] y=new long[2];
        long gcd=gcdExtended(b%a, a, y);

        x[0]=y[1]-(b/a)*y[0];
        x[1]=y[0];

        return gcd;
    }

     boolean findSum(int set[], int n, long sum)
    {
      if (sum == 0)
         return true;
      if (n == 0 && sum != 0)
         return false;
      if (set[n-1] > sum)
         return findSum(set, n-1, sum);
      return findSum(set, n-1, sum) ||findSum(set, n-1, sum-set[n-1]);
    }
   
      public static long modPow(long base, long exp, long mod)
     {
        base = base % mod;
        long result = 1;
        while (exp > 0)
       {
            if (exp % 2 == 1) 
            {
                result = (result * base) % mod;
            }
            base = (base * base) % mod;
            exp = exp >> 1;
       }
        return result;
    }
 
    static long[] fac;
    static long[] inv;
    static long mod=(long)1e9+7;
    public static void cal() 
    {
        fac = new long[1000005];
        inv = new long[1000005];
        fac[0] = 1;
        inv[0] = 1;
        for (int i = 1; i <= 1000000; i++)
        {
            fac[i] = (fac[i - 1] * i) % mod;
            inv[i] = (inv[i - 1] * modPow(i, mod - 2, mod)) % mod;
        }
    }
 
    public static long ncr(int n, int r) 
    {
        return (((fac[n] * inv[r]) % mod) * inv[n - r]) % mod;
    }

 
////////////////////////////////////////// Input Reader ////////////////////////////////////////////////////////////////////////////////////////////////////
     
    static InputReader sc = new InputReader(System.in);
    static PrintWriter out= new PrintWriter(System.out);   
    
    static class InputReader {

          private final InputStream stream;
          private final byte[] buf = new byte[8192];
          private int curChar, snumChars;
          private SpaceCharFilter filter;

          public InputReader(InputStream stream) {
                  this.stream = stream;
          }

          public int snext()
         {
                  if (snumChars == -1)
                          throw new InputMismatchException();
                  if (curChar >= snumChars) {
                          curChar = 0;
                          try {
                                  snumChars = stream.read(buf);
                          } catch (IOException e) {
                                  throw new InputMismatchException();
                          }
                          if (snumChars <= 0)
                                  return -1;
                  }
                  return buf[curChar++];
          }

          public int nextInt()
         {
                  int c = snext();
                  while (isSpaceChar(c)) 
                  {
                          c = snext();
                  }
                  int sgn = 1;
                  if (c == '-')
                  {
                          sgn = -1;
                          c = snext();
                  }
                  int res = 0;
                  do {
                          if (c < '0' || c > '9')
                                  throw new InputMismatchException();
                          res *= 10;
                          res += c - '0';
                          c = snext();
                  } while (!isSpaceChar(c));
                  return res * sgn;
          }

          public long nextLong() 
          {
                  int c = snext();
                  while (isSpaceChar(c)) 
                  {
                          c = snext();
                  }
                  int sgn = 1;
                  if (c == '-') 
                  {
                          sgn = -1;
                          c = snext();
                  }
                  long res = 0;
                  do {
                          if (c < '0' || c > '9')
                                  throw new InputMismatchException();
                          res *= 10;
                          res += c - '0';
                          c = snext();
                  } while (!isSpaceChar(c));
                  return res * sgn;
          }

          public int[] nextIntArray(int n)
          {
                  int a[] = new int[n];
                  for (int i = 0; i < n; i++) 
                  {
                          a[i] = nextInt();
                  }
                  return a;
          }

          public long[] nextLongArray(int n)
          {
                  long a[] = new long[n];
                  for (int i = 0; i < n; i++) 
                  {
                          a[i] = nextLong();
                  }
                  return a;
          }

          
          public String nextLine()
         {
                  int c = snext();
                  while (isSpaceChar(c))
                          c = snext();
                  StringBuilder res = new StringBuilder();
                  do {
                          res.appendCodePoint(c);
                          c = snext();
                  } while (!isEndOfLine(c));
                  return res.toString();
          }

          public boolean isSpaceChar(int c) 
          {
                  if (filter != null)
                          return filter.isSpaceChar(c);
                  return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
          }

          private boolean isEndOfLine(int c) 
          {
                  return c == '\n' || c == '\r' || c == -1;
          }

          public interface SpaceCharFilter 
          {
                  public boolean isSpaceChar(int ch);
          }

    }

    static int i()
    {
        return sc.nextInt();
    }
    static long l(){
        return sc.nextLong();
    }
    static int[] iarr(int n)
    {
        return sc.nextIntArray(n);
    }
    static long[] larr(int n)
    {
        return sc.nextLongArray(n);
    }
    static String s(){
        return sc.nextLine();
    }
  
 
 }