Problem Description

Background

Fatima Cynara is an analyst at Amalgamated Artichokes (AA). As with any company, AA has had some very good times as well as some bad ones. Fatima does trending analysis of the stock prices for AA, and she wants to determine the largest decline in stock prices over various time spans. For example, if over a span of time the stock prices were $19$, $12$, $13$, $11$, $20$, and $14$, then the largest decline would be $8$ between the first and fourth price. If the last price had been $10$ instead of $14$, then the largest decline would have been $10$ between the last two prices.

Fatima has done some previous analyses and has found that the stock price over any period of time can be modelled reasonably accurately with the following equation:

$$ \operatorname {price}(k) = p \cdot (\sin (a \cdot k+b) + \cos (c \cdot k+d) + 2) $$

where $p$, $a$, $b$, $c$, and $d$ are constants. Fatima would like you to write a program to determine the largest price decline over a given sequence of prices. Figure 1 illustrates the price function for Sample Input 1. You have to consider the prices only for integer values of $k$.

For Sample Input 1, the largest decline occurs from the fourth to the seventh price.

Problem Statement

For a given sequence, find the maximum difference between any two elements where the first element is greater than the second.

Input Format

The input consists of a single line containing six integers $p$ ($1 \le p \le 1000$), $a$, $b$, $c$, $d$ ($0 \le a, b, c, d \le 1000$), and $n$ ($1 \le n \le 10^6$). The first five integers are as described above, and $n$ is the length of the sequence.

Output Format

Display the maximum decline in the stock prices. If there is no decline, display the number $0$. Your output should have an absolute or relative error of at most $10^{-6}$.

Notes/Hints

Time limit: 5000 ms, Memory limit: 1048576 kB.

International Collegiate Programming Contest (ACM-ICPC) World Finals 2015

Sample Input and Output

Sample Input 1

42 1 23 4 8 10

Sample Output 1

104.855110477

Sample Input 2

100 7 615 998 801 3

Sample Output 2

0.00

Sample Input 3

100 432 406 867 60 1000

Sample Output 3

399.303813

见题面 Input 部分

见题面 Output 部分