Picture by Hans Hillewaert via Wikimedia Commons
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 $k$.
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
