Problem A
Amalgamated Artichokes
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 $k$.
![\includegraphics[width=0.9\textwidth ]{sample1}](/problems/artichoke/file/statement/en/img-0002.png)
Input
The input consists of a single line containing $6$ integers $p$ ($1 \le p \le 1\, 000$), $a$, $b$, $c$, $d$ ($0 \le a, b, c, d \le 1\, 000$) and $n$ ($1 \le n \le 10^6$). The first $5$ integers are described above. The sequence of stock prices to consider is $\operatorname {price(1)}, \operatorname {price(2)}, \ldots , \operatorname {price}(n)$.
Output
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 $10^{-6}$.
| Sample Input 1 | Sample Output 1 |
|---|---|
42 1 23 4 8 10 |
104.855110477 |
| Sample Input 2 | Sample Output 2 |
|---|---|
100 7 615 998 801 3 |
0.00 |
| Sample Input 3 | Sample Output 3 |
|---|---|
100 432 406 867 60 1000 |
399.303813 |