write a go solution for Description:
You are an ambitious king who wants to be the Emperor of The Reals. But to do that, you must first become Emperor of The Integers.

Consider a number axis. The capital of your empire is initially at 0. There are n unconquered kingdoms at positions 0<x_1<x_2<ldots<x_n. You want to conquer all other kingdoms.

There are two actions available to you:

- You can change the location of your capital (let its current position be c_1) to any other conquered kingdom (let its position be c_2) at a cost of a*|c_1-c_2|.
- From the current capital (let its current position be c_1) you can conquer an unconquered kingdom (let its position be c_2) at a cost of b*|c_1-c_2|. You cannot conquer a kingdom if there is an unconquered kingdom between the target and your capital.

Note that you cannot place the capital at a point without a kingdom. In other words, at any point, your capital can only be at 0 or one of x_1,x_2,ldots,x_n. Also note that conquering a kingdom does not change the position of your capital.

Find the minimum total cost to conquer all kingdoms. Your capital can be anywhere at the end.

Input Format:
The first line contains a single integer t (1<=t<=1000)  — the number of test cases. The description of each test case follows.

The first line of each test case contains 3 integers n, a, and b (1<=qn<=q2*10^5; 1<=a,b<=10^5).

The second line of each test case contains n integers x_1,x_2,ldots,x_n (1<=x_1<x_2<ldots<x_n<=10^8).

The sum of n over all test cases does not exceed 2*10^5.

Output Format:
For each test case, output a single integer  — the minimum cost to conquer all kingdoms.

Note:
Here is an optimal sequence of moves for the second test case:

1. Conquer the kingdom at position 1 with cost 3*(1-0)=3.
2. Move the capital to the kingdom at position 1 with cost 6*(1-0)=6.
3. Conquer the kingdom at position 5 with cost 3*(5-1)=12.
4. Move the capital to the kingdom at position 5 with cost 6*(5-1)=24.
5. Conquer the kingdom at position 6 with cost 3*(6-5)=3.
6. Conquer the kingdom at position 21 with cost 3*(21-5)=48.
7. Conquer the kingdom at position 30 with cost 3*(30-5)=75.

The total cost is 3+6+12+24+3+48+75=171. You cannot get a lower cost than this.. Output only the code with no comments, explanation, or additional text.