Arpa and a list of numbers

我们认为一个序列是bad序列，当且仅当该序列非空且gcd是1。现在有两种操作： 1、删除一个数，代价为x。 2、给一个数+1，代价为y。 现给出该序列和x，y，求将给定序列变为good序列（非bad）的最小代价。 翻译贡献者UID：6496

Arpa has found a list containing $ n $ numbers. He calls a list bad if and only if it is not empty and gcd (see notes section for more information) of numbers in the list is $ 1 $ . Arpa can perform two types of operations: - Choose a number and delete it with cost $ x $ . - Choose a number and increase it by $ 1 $ with cost $ y $ . Arpa can apply these operations to as many numbers as he wishes, and he is allowed to apply the second operation arbitrarily many times on the same number. Help Arpa to find the minimum possible cost to make the list good.

First line contains three integers $ n $ , $ x $ and $ y $ ( $ 1<=n<=5·10^{5} $ , $ 1<=x,y<=10^{9} $ ) — the number of elements in the list and the integers $ x $ and $ y $ . Second line contains $ n $ integers $ a_{1},a_{2},...,a_{n} $ ( $ 1<=a_{i}<=10^{6} $ ) — the elements of the list.

Print a single integer: the minimum possible cost to make the list good.

4 23 17
1 17 17 16

40

10 6 2
100 49 71 73 66 96 8 60 41 63

10

In example, number $ 1 $ must be deleted (with cost $ 23 $ ) and number $ 16 $ must increased by $ 1 $ (with cost $ 17 $ ). A gcd (greatest common divisor) of a set of numbers is the maximum integer that divides all integers in the set. Read more about gcd [here](https://en.wikipedia.org/wiki/Greatest_common_divisor).