Kevin is dissatisfied with his current grades. So, he hacks into the school's grading system to give himself some extra points! However, he can only give himself at most $K$ points across all $N$ of his courses before his teachers get suspicious.

His grades are represented as fractions, each with a numerator $a_i$ that is less than or equal to the denominator $b_i$. When Kevin adds a point to a grade, both the numerator and the denominator increase by one.

In order to maximize the chances of getting into a good university, Kevin wants to make sure that the average of all his grades is as large as possible. Can you help Kevin with this task?

Constraints

$1\le N,K\le 2\times {10}^5$

$1\le a_i\le b_i\le {10}^9$

Input Specification

On the first line, you are given two space-separated integers, $N$ and $K$.

The second line will contain $N$ space-separated integers $a_i$, each describing the numerator of Kevin's grade in the $i$-th course.

The third line will contain $N$ space-separated integers $b_i$, each describing the denominator of Kevin's grade in the $i$-th course.

Output Specification

Output a single number: the maximum average grade Kevin can obtain as a percentage. Your answer will be considered correct if it is within ${10}^{-6}$ of the actual answer.

Sample Input 1

3 2
1 2 3
2 5 3

Sample Output 1

72.2222222

Explanation for Sample 1

You can add one points to the first course, making it $\frac{2}{3}$, then add one point to the second course, making it $\frac{3}{6}$. Then, the average score is $\frac{0.666+0.5+1}{3}\approx 0.72222222$, which, as a percent, is $72.222222\mathrm{\%}$. It can be proven that this solution is optimal.

Sample Input 2

5 100
2 5 9 9 3
10 50 22 51 9

Sample Output 2

59.7345122