CF42A.Guilty — to the kitchen!

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 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?

今天对沃洛佳来说是非常不幸的一天。他在代数课上得了低分，因此被迫在厨房里做些事情—— namely 煮罗宋汤（一道传统的俄罗斯汤）。这也有助于提高他的代数能力。

根据罗宋汤的食谱，该汤由 $n$ 种原料组成，需按比例 $\frac{a_1}{a_1 + a_2 + \dots + a_n} : \frac{a_2}{a_1 + a_2 + \dots + a_n} : \dots : \frac{a_n}{a_1 + a_2 + \dots + a_n}$（即总量为 $1$ 升）混合（因此，对应原料的用量应分别为 $a_1 \cdot x,\, ..., \, a_n \cdot x$ 升，其中 $x \ge 0$）。沃洛佳在厨房中发现，他手头恰好分别有 $b_1,\, ..., \, b_n$ 升这些原料。为了弥补代数上的失误，他必须在一个容量为 $V$ 升的锅中尽可能多地煮汤（即所煮汤的体积必须介于 $0$ 到 $V$ 升之间）。沃洛佳最终能煮出多少升罗宋汤？

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).

输入的第一行包含两个用空格分隔的整数 $n$ 和 $V$（$1 ≤ n ≤ 20$，$1 ≤ V ≤ 10000$）。
第二行包含 $n$ 个用空格分隔的整数 $a_i$（$1 ≤ a_i ≤ 100$）。
最后一行包含 $n$ 个用空格分隔的整数 $b_i$（$0 ≤ b_i ≤ 100$）。

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.

你的程序应仅输出一个实数——即沃洛佳将烹制的汤的体积。你的答案必须满足相对误差或绝对误差小于 $10^{-4}$。