# Disco

Anton, as a teacher at school, is organizing a disco for the children. He has been tasked with selecting a playlist so that everyone is thrilled with the celebration. But Anton has a huge database of songs, and unfortunately, the time for the disco is limited :(.

Specifically, there are $n$ songs in the database. Each song can be characterized by two integers $t_{i}$ and $r_{i}$ — the length of the song and its rating. As a music lover, Anton wants to select exactly $k$ songs (i.e., not fewer) to maximize the ratio of the sum of ratings to the sum of lengths.

More formally, let $S$ be the set of songs and $X⊆S$, $∣X∣=k$ — a subset of songs that have been selected for the playlist. The goal is to maximize $∑_{i∈X}t_{i}∑_{i∈X}r_{i} $. In other words, it is necessary to find the sum of the numbers $r_{i}$ of all the songs that will be played at the disco, find the sum of the numbers $t_{i}$ of all the songs that will be played at the disco, and divide the former by the latter. This number needs to be maximized.

Find and output the maximum possible ratio.

## Input

The first line contains two integers $n$, $k$ ($1≤k≤n≤10_{5}$) — the total number of songs and the number of songs to be selected for the playlist.

The second line contains $n$ integers $r_{i}$ ($1≤r_{i}≤10_{5}$).

The third line contains $n$ integers $t_{i}$ ($1≤t_{i}≤10_{5}$).

## Output

Output a single number — the maximum ratio.

Your answer will be considered correct if its absolute or relative error does not exceed $10_{−4}$.

Formally, let your answer be $a$, and the jury's answer be $b$. Your answer will be accepted if and only if $max(1,∣b∣)∣a−b∣ ≤10_{−4}$.

## Examples

## Note

In the first example, there are two songs that need to be added to the playlist. Therefore, the ratio will be:

In the second example, it is best to take the third and fifth songs. Therefore, the ratio will be: