Author:  M. Sporyshev  Time limit:  1 sec  
Input file:  input.txt  Memory limit:  256 Mb  
Output file:  output.txt 
Young programmer Vasya decided to start running every morning to keep himself in a good shape.
Vasya googled how to run properly if you have lead a sedentary lifestyle for too long and found an article where the following technique was offered.
You need to run along a circular track divided into N segments. Length of ith segment is a_{i} meters.
One should alternate slow and fast running: on the first, third and following odd segments — with the speed of V m/s, on the second, fourth and following even segments — with the speed of 2 V m/s.
Vasya wondered how far he would run in T seconds, given the sequence of segment lengths and the starting speed.
The first line of the input file contains integers N, V, T — the number of segments, the initial speed and the time that Vasya will run for.
The second line of the input file contains integers a_{i} — lengths of the segments along the track. The sum of the lengths of the segments is equal to the length of the track.
Output file must contain a single number — the distance that Vasya will run in the specified time with an accuracy of at least 5 digits after the decimal point.
1 ≤ N ≤ 10^{4}
1 ≤ a_{i} ≤ 10^{4}
1 ≤ V, T ≤ 10^{4}
No.  Input file (input.txt ) 
Output file (output.txt ) 

1 


2 

