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.lang.Math.*;

public class MainA {

	public static int mod = 20000;
	public static long[] val;
	public static long[] arr;
	static int max = (int) 1e9 + 7;

	public static void main(String[] args) {

		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n=in.nextInt();
		long w=in.nextLong();
		
		long arr[]=new long[2*n];
		for(int i=0;i<2*n;i++)arr[i]=in.nextLong();
		
		Arrays.sort(arr);
		long mg=arr[0],mb=arr[n];
		double gg,bg;
		double x=(double)w/(n*3);
		double y=(double)mb/2;
		gg=Math.min(mg, x);gg=Math.min(y,gg);bg=2*gg;
		out.printf("%.7f",n*(gg+bg));
		
		out.close();
	}

	static void swap(Pairs arr[], int i, int j) {
		Pairs t = arr[i];
		arr[i] = arr[j];
		arr[j] = t;
	}

	static int partition(Pairs arr[], int l, int h) {
		long x = arr[h].x;
		int i = (l - 1);

		for (int j = l; j <= h - 1; j++) {
			if (arr[j].x <= x) {
				i++;
				// swap arr[i] and arr[j]
				swap(arr, i, j);
			}
		}
		// swap arr[i+1] and arr[h]
		swap(arr, i + 1, h);
		return (i + 1);
	}

	// Sorts arr[l..h] using iterative QuickSort
	static void sort(Pairs arr[], int l, int h) {
		// create auxiliary stack
		int stack[] = new int[h - l + 1];

		// initialize top of stack
		int top = -1;

		// push initial values in the stack
		stack[++top] = l;
		stack[++top] = h;

		// keep popping elements until stack is not empty
		while (top >= 0) {
			// pop h and l
			h = stack[top--];
			l = stack[top--];

			// set pivot element at it's proper position
			int p = partition(arr, l, h);

			// If there are elements on left side of pivot,
			// then push left side to stack
			if (p - 1 > l) {
				stack[++top] = l;
				stack[++top] = p - 1;
			}

			// If there are elements on right side of pivot,
			// then push right side to stack
			if (p + 1 < h) {
				stack[++top] = p + 1;
				stack[++top] = h;
			}
		}
	}

	static class Pairs implements Comparable<Pairs> {
		long x;
		int y;

		Pairs(long a, int b) {
			x = a;
			y = b;
		}

		@Override
		public int compareTo(Pairs o) {
			// TODO Auto-generated method stub
			if (x == o.x)
				return Integer.compare(y, o.y);
			else
				return Long.compare(x, o.x);
		}

	}

	public static void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	public 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;
	}

	public static String rev(String s) {
		StringBuilder sb = new StringBuilder(s);
		sb.reverse();
		return sb.toString();
	}

	public static long gcd(long x, long y) {
		if (y == 0)
			return x;
		if (x % y == 0)
			return y;
		else
			return gcd(y, x % y);
	}

	public static int gcd(int x, int y) {
		if (x % y == 0)
			return y;
		else
			return gcd(y, x % y);
	}

	public 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;
	}

	public static int abs(int a, int b) {
		return (int) Math.abs(a - b);
	}

	public static long abs(long a, long b) {
		return (long) Math.abs(a - b);
	}

	public static int max(int a, int b) {
		if (a > b)
			return a;
		else
			return b;
	}

	public static int min(int a, int b) {
		if (a > b)
			return b;
		else
			return a;
	}

	public static long max(long a, long b) {
		if (a > b)
			return a;
		else
			return b;
	}

	public static long min(long a, long b) {
		if (a > b)
			return b;
		else
			return a;
	}

	public static long[][] mul(long a[][], long b[][]) {
		long c[][] = new long[2][2];
		c[0][0] = a[0][0] * b[0][0] + a[0][1] * b[1][0];
		c[0][1] = a[0][0] * b[0][1] + a[0][1] * b[1][1];
		c[1][0] = a[1][0] * b[0][0] + a[1][1] * b[1][0];
		c[1][1] = a[1][0] * b[0][1] + a[1][1] * b[1][1];

		return c;
	}

	public static long[][] pow(long n[][], long p, long m) {
		long result[][] = new long[2][2];
		result[0][0] = 1;
		result[0][1] = 0;
		result[1][0] = 0;
		result[1][1] = 1;

		if (p == 0)
			return result;
		if (p == 1)
			return n;
		while (p != 0) {
			if (p % 2 == 1)
				result = mul(result, n);
			//System.out.println(result[0][0]);
			for (int i = 0; i < 2; i++) {
				for (int j = 0; j < 2; j++) {
					if (result[i][j] >= m)
						result[i][j] %= m;
				}
			}

			p >>= 1;
			n = mul(n, n);
			// System.out.println(1+" "+n[0][0]+" "+n[0][1]+" "+n[1][0]+" "+n[1][1]);
			for (int i = 0; i < 2; i++) {
				for (int j = 0; j < 2; j++) {
					if (n[i][j] >= m)
						n[i][j] %= m;
				}
			}
		}
		return result;
	}

	public static long pow(long n, long p) {
		long result = 1;
		if (p == 0)
			return 1;
		if (p == 1)
			return n;
		while (p != 0) {
			if (p % 2 == 1)
				result *= n;
			p >>= 1;
			n *= n;
		}
		return result;
	}

	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] = nextInt();
			}
			return a;
		}

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

		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);
		}
	}
}