Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Guilty — to the kitchen!

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIt'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 litres (thus, there should be *a*_{1} ·*x*, ..., *a*_{n} ·*x* litres of corresponding ingredients mixed for some non-negative *x*). In the kitchen Volodya found out that he has *b*_{1}, ..., *b*_{n} 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 *a*_{i} (1 ≤ *a*_{i} ≤ 100). Finally, the last line contains *n* space-separated integers *b*_{i} (0 ≤ *b*_{i} ≤ 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

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/25/2017 05:37:14 (c2).

Desktop version, switch to mobile version.

User lists

Name |
---|