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 \leq N, K \leq 2 \times 10^5~

~1 \leq a_i \leq b_i \leq 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\%~. 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