Problem Description

A hedger is an investor who takes steps to reduce the risk of investment by doing appropriate research and analysis of stocks. Assume that you are a hedger.

Now you have been given some parameters based on which you have to analyse and pick the correct stocks. You have been assigned a fund that you have to manage in such a way that it should give maximum returns.

According to your research you have a list of stocks for which you know the corresponding profit percentage that you can earn within a certain horizon. Being a hedger, you don’t want to pull all your eggs in one basket. That’s why you have decided the upper limit in terms of quantity that you will buy.

Given number of stocks, the upper limit on quantity per stock, the amount to be invested, the list of stock prices and list of expected profit percentages, calculate the maximum profit you can make.

Note: All computations should be up to two digits after the decimal point.

Constraints

0 <= A <= 10^6

1 <=K <= 100

1 <= N <= 10^4

Input

First line contains three space separated integers N K A where N is number of stocks you are interested in, K is maximum quantity of any particular stock you can buy and A is capita; amount you have.

Second line contains N space separated decimals denoting the prices of stocks.

Third line contains N space separated decimals denoting the profit percentages corresponding to the index of stock prices.

Output

Print the maximum profit that can be earned from the given amount, rounded to the nearest integer

Time Limit

1

Examples

Example 1

Input

4 2 100

20 10 30 40

5 10 30 20

Output

26

Explanation

Here, we can select only two quantities of any stock that we choose to buy. We choose to buy stocks which are priced at 0 and 40 respectively before we exhaust our capital. The maximum profit that can be earned

Profit = 2*((30*30)/100)+1*(40*20)/100)=26