WORKB - Working in Beijing

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Mr. M is an undergraduate student of FDU. He finds an intern position in Beijing, so that he cannot attend all the college activities. But in some conditions, he must come back to Shanghai on certain date. We can assume the important activities that Mr. M must attend are occupy a whole day. Mr. M must take flight to Shanghai before that day and leave after that day. On the other hand, Mr. M is absent in Beijing and he will lose his salary for his absent.

Sometimes the cost of flight is much higher than the loss of salary, so to save the cost on the travel, Mr. M can stay in Shanghai to wait for another important date before he back to Beijing.

Now, Mr. M knows all of the important date in the next year. Help him schedule his travel to optimize the cost.

Input

The input contains several test cases. The first line of single integer indicates the number of test cases.

For each test case, the first line contains three integers: n, a and b, denoting the number of important events, the cost of a single flight from Beijing to Shanghai or Shanghai to Beijing and the salary for a single day stay in Beijing. (1 <= n <= 100000, 1 <= a <= 1000000000, 1 <= b <=100)

Next line contains n integers ti, denoting the time of the important events. You can assume the ti are in increasing order and they are different from each other. (0 <= ti <= 10000000)

Output

For each test case, output a single integer indicating the minimum cost for this year.

Example

Input:
2
1 10 10
5
5 10 2
5 10 15 65 70

Output:
Case #1: 30
Case #2: 74

Warning: large input/output data, be careful with certain languages.


hide comments
vas14: 2021-11-23 00:29:02

He starts at work and must end up at work.

Shubham: 2015-01-11 16:02:55

Make sure to put ans in Case #i format :)
caused me 2 WA...;(

`Ak: 2014-05-22 13:52:57

nice prob ....
silly mistake costed 6 wa :( :(
finally got ac :) :)

Last edit: 2014-05-22 14:15:03
Trishla Sancheti: 2014-05-10 14:11:46

why is it getting TLE ..?? using normal logic

BLANKRK: 2013-06-27 17:23:14

nice prob....
AC in frst attmpt :)

:-): 2013-04-22 17:33:43

good problem

raunakrocks: 2013-04-12 15:05:21

AC!!

The Mundane Programmer: 2013-03-13 23:39:25

Easy One


Added by:Fudan University Problem Setters
Date:2011-09-08
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Fudan University Local Contest #3, by lcosvse