# Dropping tests

Time Limit: 1000MS Memory Limit: 65536K

## Description

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

$$100*\frac{\sum_{i=1}^na_i}{\sum_{j=1}^nb_j}$$

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 $100*\frac{5+0+2}{5+1+6}=50$. However, if you drop the third test, your cumulative average becomes $100*\frac{5+0}{5+1}\approx 83.33$.

## Input

The input test file will contain multiple test cases, each containing exactly three lines. The first line contains two integers, 1 ≤ n ≤ 1000 and 0 ≤ k < n. The second line contains n integers indicating ai for all i. The third line contains n positive integers indicating bi for all i. It is guaranteed that 0 ≤ ai ≤ bi ≤ 1, 000, 000, 000. The end-of-file is marked by a test case with n = k = 0 and should not be processed.

## Output

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.

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

83
100

## Hint

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).

## 算法分析

01分数规划问题主要包含一般的01分数规划、最优比率生成树问题、最优比率环问题等。

$$R=\frac{\sum(a[i]*x[i])}{\sum(b[i]*x[i])}$$

$$F(L)=\sum(a[i]*x[i])-L*\sum(b[i]*x[i])$$

$$F(L)=\sum((a[i]-L*b[i])*x[i])$$

$$F(L)=\sum(d[i]*x[i])$$

1. F(L)单调递减

2. F(max(L)/min(L)) = 0

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