3207. Dropping tests

In a certain course, you take $n$ tests. If you get $a_i$ out of $b_i$ questions correct on test $i$, your cumulative average is defined to be

$$100 \cdot \frac{\sum_{i=1}^n a_i}{\sum_{i=1}^n b_i}$$

Given your test scores and a positive integer $k$, determine how high you can make your cumulative average if you are allowed to drop any $k$ of your test scores.

Suppose you take $3$ tests with scores of $5/5$, $0/1$, and $2/6$. Without dropping any tests, your cumulative average is $100\cdot \frac{5+0+2}{5+1+6} = 50$. However, if you drop the third test, your cumulative average becomes $100 \cdot \frac{5+0}{5+1} \approx 83.33 \approx 83$.

输入格式

The input test file will contain multiple test cases, each containing exactly three lines. The first line contains two integers, $1 \leq n \leq 1000$ and $0 \leq k < n$. The second line contains $n$ integers indicating $a_i$ for all $i$. The third line contains $n$ positive integers indicating $b_i$ for all $i$. It is guaranteed that $0 \leq a_i \leq b_i \leq 10^9$. The end-of-file is marked by a test case with $n = k = 0$ and should not be processed.

输出格式

For each test case, write a single line with the highest cumulative average possible after dropping $k$ of the given test scores. The average should be rounded to the nearest integer.

样例

Input
3 1
5 0 2
5 1 6
4 2
1 2 7 9
5 6 7 9
0 0

Output
83
100


提示

To avoid ambiguities due to rounding errors, the judge tests have been constructed so that all answers are at least $0.001$ away from a decision boundary (i.e., you can assume that the average is never $83.4997$).

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