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 x[i].

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 ≤ 10^5), a and b (1 ≤ a, b ≤ 10^9). Next line contains n integers x[1], x[2], ... , x[n] (1 ≤ x[i] ≤ 10^9). For all i (1 ≤ i ≤ n – 1) holds inequality x[i] < x[i+1].

Output

Print the lowest possible level of fatigue, at which you will visit all the cities.

Examples

Note

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.