Journey from west to east
Journey from west to east
There are n cities standing on a straight line from west to east. The cities are numbered from 1 to n, in order from west to east. Each point on the line has its own one-dimensional coordinate, and the point closer to the east has a large coordinate. The coordinate of the i-th city is xi
.
You are now in city 1, and want to visit all cities. You have two ways to travel:
- Walk in a straight line. At the same time, your level of fatigue will increase by a units each time you move a distance of 1, regardless of the direction.
- Teleport to any point you want. Your fatigue level will increase by b units, regardless of teleported distance.
Input
First line contains three numbers n (2 ≤ n ≤ 105
), a and b (1 ≤ a, b ≤ 109
). Next line contains n integers x1
, x2
, ... , xn
(1 ≤ xi
≤ 109
). For all i (1 ≤ i ≤ n – 1) holds inequality xi
< xi+1
.
Output
Print the lowest possible level of fatigue, at which you will visit all the cities.
Explanation
Test 1.
From city 1 we go to 2-nd, then teleport to 3-rd. Then go to 4-th. The level of fatigue at the end will be equal to 2 * 1 + 5 + 2 * 2 = 11, what is the lowest possible.
Test 3.
Visit all cities, in any order, teleporting six times. The level of fatigue will be equal to 12, which is the lowest possible.
4 2 5 1 2 5 7
11
6 3 7 1 3 6 10 11 13
29
7 1 2 24 35 40 68 72 99 103
12