Minimum Ticket Cost

You are a tourist planning to explore a city over n days. On the i^th day, you need to take a_i train rides. There are two types of train tickets available:

• Single Ride Ticket: Costs x dollars and allows you to ride one train.
• One-Day Ticket: Costs y dollars and allows unlimited train rides for that day.

Your task is to determine the minimum total cost of purchasing the tickets over all n days.

The cost for each day is calculated as follows:

\[ \text{cost}_{i} = \min(a_i \times x,\ y) \quad \text{for } i = 1, 2, \dots, n \]

The answer is the sum of the daily costs.

inputFormat

The first line contains three integers n, x, and y (1 ≤ n ≤ 10⁵, 1 ≤ x, y ≤ 10⁹).

The second line contains n integers a₁, a₂, ..., a_n (0 ≤ a_i ≤ 10⁹), where a_i denotes the number of train rides on the i^th day.

outputFormat

Output a single integer representing the minimum total cost required to purchase the train tickets for all days.

sample

3 2 5
1 3 1

10