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.util.*;
import java.io.*;
public class a {
public static void main(String[] args) throws IOException
{
  input.init(System.in);
  PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));

  int n = input.nextInt(), t = input.nextInt();
  int[] as = new int[n], bs = new int[n];
  for(int i = 0; i<n; i++) as[i] = input.nextInt();
  for(int i = 0; i<n; i++) bs[i] = input.nextInt();
  double min = 1.*bs[0]/as[0];
  for(int i = 1; i<n; i++) min = Math.min(min, 1.*bs[i]/as[i]);
  double res = 0;
  for(int i = 0; i<n; i++) res += as[i]*min;
  out.println(Math.min(res, t));

  out.close();

}
static class input {
  static BufferedReader reader;
  static StringTokenizer tokenizer;

  /** call this method to initialize reader for InputStream */
  static void init(InputStream input) {
      reader = new BufferedReader(
                   new InputStreamReader(input) );
      tokenizer = new StringTokenizer("");
  }

  /** get next word */
  static String next() throws IOException {
      while ( ! tokenizer.hasMoreTokens() ) {
          //TODO add check for eof if necessary
          tokenizer = new StringTokenizer(
                 reader.readLine() );
      }
      return tokenizer.nextToken();
  }

  static int nextInt() throws IOException {
      return Integer.parseInt( next() );
  }

  static double nextDouble() throws IOException {
      return Double.parseDouble( next() );
  }
  static String nextLine() throws IOException {
    return reader.readLine();
  }
}
}