Anthony recently started watching YouTube videos with the
title “ but every time
happens it speeds up
by ”. He likes watching
these videos because it saves time, but he wonders how much
time he actually saves by watching these videos (instead of the
originals).
You may assume that the new video is exactly the same as the
original video , except
certain segments of the new video play faster. Each time event
happens, speeds up by %. Suppose event happens times in , and it happens at timestamps
(in seconds). That means the segment is playing at original
speed, the segment is playing at % speed, the segment
is playing at
% speed, and so
on. Also, is
seconds long.
Can you help Anthony compute the original length of the
video?
Input
The first line of the input contains three integers
. It is
guaranteed that , , and .
The next line of the input contains integers , denoting the timestamp of the
event . It is
guaranteed that the timestamps are given in chronological
order, and that .
Output
A single number
denoting the length of the original video in seconds. Your
answer is considered correct if its absolute or relative error
is at most .
Sample Input 1 |
Sample Output 1 |
2 20 15
3 10
|
18.400
|
Sample Input 2 |
Sample Output 2 |
1 100 5
5
|
5.00
|