Walk and Teleport

There are N towns on a line running east-west. The towns are numbered 1 through N, in order from west to east. Each point on the line has a one-dimensional coordinate, and a point that is farther east has a greater coordinate value. The coordinate of town i is X_i.

You are now at town 1, and you want to visit all the other towns. You have two ways to travel:

• Walk on the line. Your fatigue level increases by A each time you travel a distance of 1, regardless of direction.

• Teleport to any location of your choice. Your fatigue level increases by B, regardless of the distance covered.

Find the minimum possible total increase of your fatigue level when you visit all the towns in these two ways.

Constraints

• All input values are integers.
• 2≤N≤10^5
• 1≤X_i≤10^9
• For all i(1≤i≤N-1), X_i<X_{i+1}.
• 1≤A≤10^9
• 1≤B≤10^9

Input

The input is given from Standard Input in the following format:

N A B X_1 X_2 ... X_N

Output

Print the minimum possible total increase of your fatigue level when you visit all the towns.

Examples

Input

4 2 5 1 2 5 7

Output

11

Input

7 1 100 40 43 45 105 108 115 124

Output

84

Input

7 1 2 24 35 40 68 72 99 103

Output

12

inputFormat

input values are integers.

• 2≤N≤10^5
• 1≤X_i≤10^9
• For all i(1≤i≤N-1), X_i<X_{i+1}.
• 1≤A≤10^9
• 1≤B≤10^9

Input

The input is given from Standard Input in the following format:

N A B X_1 X_2 ... X_N

outputFormat

Output

Print the minimum possible total increase of your fatigue level when you visit all the towns.

Examples

Input

4 2 5 1 2 5 7

Output

11

Input

7 1 100 40 43 45 105 108 115 124

Output

84

Input

7 1 2 24 35 40 68 72 99 103

Output

12

样例

7 1 100
40 43 45 105 108 115 124

84