Problem: It's a very unfortunate day for Volodya today. He got bad mark in algebra and was therefore forced to do some work in the kitchen, namely to cook borscht (traditional Russian soup). This should also improve his algebra skills.

According to the borscht recipe it consists of n ingredients that have to be mixed in proportion <image> litres (thus, there should be a1 ·x, ..., an ·x litres of corresponding ingredients mixed for some non-negative x). In the kitchen Volodya found out that he has b1, ..., bn litres of these ingredients at his disposal correspondingly. In order to correct his algebra mistakes he ought to cook as much soup as possible in a V litres volume pan (which means the amount of soup cooked can be between 0 and V litres). What is the volume of borscht Volodya will cook ultimately?

Input

The first line of the input contains two space-separated integers n and V (1 ≤ n ≤ 20, 1 ≤ V ≤ 10000). The next line contains n space-separated integers ai (1 ≤ ai ≤ 100). Finally, the last line contains n space-separated integers bi (0 ≤ bi ≤ 100).

Output

Your program should output just one real number — the volume of soup that Volodya will cook. Your answer must have a relative or absolute error less than 10 - 4.

Examples

Input

1 100
1
40


Output

40.0


Input

2 100
1 1
25 30


Output

50.0


Input

2 100
1 1
60 60


Output

100.0

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.lang.reflect.Constructor;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.StringTokenizer;

public class MartesG 
{
	static class Scanner
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		
		public String nextLine()
		{
			try
			{
				return br.readLine();
			}
			catch(Exception e)
			{
				throw(new RuntimeException());
			}
		}
		
		public String next()
		{
			while(!st.hasMoreTokens())
			{
				String l = nextLine();
				if(l == null)
					return null;
				st = new StringTokenizer(l);
			}
			return st.nextToken();
		}
		
		public int nextInt()
		{
			return Integer.parseInt(next());
		}
		
		public long nextLong()
		{
			return Long.parseLong(next());
		}
		
		public double nextDouble()
		{
			return Double.parseDouble(next());
		}
		
		public int[] nextIntArray(int n)
		{
			int[] res = new int[n];
			for(int i = 0; i < res.length; i++)
				res[i] = nextInt();
			return res;
		}
		
		public long[] nextLongArray(int n)
		{
			long[] res = new long[n];
			for(int i = 0; i < res.length; i++)
				res[i] = nextLong();
			return res;
		}
		
		public double[] nextDoubleArray(int n)
		{
			double[] res = new double[n];
			for(int i = 0; i < res.length; i++)
				res[i] = nextDouble();
			return res;
		}
		public void sortIntArray(int[] array)
		{
			Integer[] vals = new Integer[array.length];
			for(int i = 0; i < array.length; i++)
				vals[i] = array[i];
			Arrays.sort(vals);
			for(int i = 0; i < array.length; i++)
				array[i] = vals[i];
		}
		
		public void sortLongArray(long[] array)
		{
			Long[] vals = new Long[array.length];
			for(int i = 0; i < array.length; i++)
				vals[i] = array[i];
			Arrays.sort(vals);
			for(int i = 0; i < array.length; i++)
				array[i] = vals[i];
		}
		
		public void sortDoubleArray(double[] array)
		{
			Double[] vals = new Double[array.length];
			for(int i = 0; i < array.length; i++)
				vals[i] = array[i];
			Arrays.sort(vals);
			for(int i = 0; i < array.length; i++)
				array[i] = vals[i];
		}

		public String[] nextStringArray(int n) 
		{	
			String[] vals = new String[n];
			for(int i = 0; i < n; i++)
				vals[i] = next();
			return vals;
		}
		
		public Integer nextInteger()
		{
			String s = next();
			if(s == null)
				return null;
			return Integer.parseInt(s);
		}
		
		public int[][] nextIntMatrix(int n, int m)
		{
			int[][] ans = new int[n][];
			for(int i = 0; i < n; i++)
				ans[i] = nextIntArray(m);
			return ans;
		}
		
		public char[][] nextGrid(int r) 
		{
			char[][] grid = new char[r][];
			for(int i = 0; i < r; i++)
				grid[i] = next().toCharArray();
			return grid;
		}
		
		public static <T> T fill(T arreglo, int val)
		{
			if(arreglo instanceof Object[])
			{
				Object[] a = (Object[]) arreglo;
				for(Object x : a)
					fill(x, val);
			}
			else if(arreglo instanceof int[])
				Arrays.fill((int[]) arreglo, val);
			else if(arreglo instanceof double[])
				Arrays.fill((double[]) arreglo, val);
			else if(arreglo instanceof long[])
				Arrays.fill((long[]) arreglo, val);
			return arreglo;
		}
		
		<T> T[] nextObjectArray(Class <T> clazz, int size)
		{
			@SuppressWarnings("unchecked")
			T[] result = (T[]) java.lang.reflect.Array.newInstance(clazz, size);
			for(int c = 0; c < 3; c++)
			{
				Constructor <T> constructor;
				try 
				{
					if(c == 0)
						constructor = clazz.getDeclaredConstructor(Scanner.class, Integer.TYPE);
					else if(c == 1)
						constructor = clazz.getDeclaredConstructor(Scanner.class);
					else
						constructor = clazz.getDeclaredConstructor();
				} 
				catch(Exception e)
				{
					continue;
				}
				try
				{
					for(int i = 0; i < result.length; i++)
					{
						if(c == 0)
							result[i] = constructor.newInstance(this, i);
						else if(c == 1)
							result[i] = constructor.newInstance(this);
						else
							result[i] = constructor.newInstance();	
					}
				}
				catch(Exception e)
				{
					throw new RuntimeException(e);
				}
				return result;
			}
			throw new RuntimeException("Constructor not found");
		}
		
		public void printLine(int... vals)
		{
			if(vals.length == 0)
				System.out.println();
			else
			{
				System.out.print(vals[0]);
				for(int i = 1; i < vals.length; i++)
					System.out.print(" ".concat(String.valueOf(vals[i])));
				System.out.println();
			}
		}
		
		public void printLine(long... vals)
		{
			if(vals.length == 0)
				System.out.println();
			else
			{
				System.out.print(vals[0]);
				for(int i = 1; i < vals.length; i++)
					System.out.print(" ".concat(String.valueOf(vals[i])));
				System.out.println();
			}
		}
		
		public void printLine(double... vals)
		{
			if(vals.length == 0)
				System.out.println();
			else
			{
				System.out.print(vals[0]);
				for(int i = 1; i < vals.length; i++)
					System.out.print(" ".concat(String.valueOf(vals[i])));
				System.out.println();
			}
		}
		
		public void printLine(int prec, double... vals)
		{
			if(vals.length == 0)
				System.out.println();
			else
			{
				System.out.printf("%." + prec + "f", vals[0]);
				for(int i = 1; i < vals.length; i++)
					System.out.printf(" %." + prec + "f", vals[i]);
				System.out.println();
			}
		}
		
		public Collection <Integer> wrap(int[] as)
		{
			ArrayList <Integer> ans = new ArrayList <Integer> ();
			for(int i : as)
				ans.add(i);
			return ans;
		}
		
		public int[] unwrap(Collection <Integer> collection)
		{
			int[] vals = new int[collection.size()];
			int index = 0;
			for(int i : collection) vals[index++] = i;
			return vals;
		}
	}
	
	static int v;
	static int[] ingredients;
	static int[] limits;
	
	static double binarySearch(double a, double b)
	{
		double mid = (a + b) / 2;
		if(mid == a || mid == b) return mid;
		boolean ok = true;
		double total = 0;
		for(int i = 0; i < ingredients.length; i++)
		{
			double used = ingredients[i] * mid;
			if(used > limits[i])
				ok = false;
			total += used;
		}
		ok = ok && total <= v;
		if(!ok)
			return binarySearch(a, mid);
		else
			return binarySearch(mid, b);
	}
	
	public static void main(String[] args)
	{
		Scanner sc = new Scanner();
		int n = sc.nextInt();
		v = sc.nextInt();
		ingredients = sc.nextIntArray(n);
		limits = sc.nextIntArray(n);
		double result = 0;
		double x = binarySearch(0, v);
		for(int i : ingredients)
			result += i * x;
		sc.printLine(result);
	}
}