Number Transformation II

You are given a sequence of positive integers x₁, x₂, ..., x_n and two non-negative integers a and b. Your task is to transform a into b. To do that, you can perform the following moves:

• subtract 1 from the current a;
• subtract a mod x_i (1 ≤ i ≤ n) from the current a.

Operation a mod x_i means taking the remainder after division of number a by number x_i.

Now you want to know the minimum number of moves needed to transform a into b.

The first line contains a single integer n (1 ≤  n ≤ 10⁵). The second line contains n space-separated integers x₁, x₂, ..., x_n (2 ≤  x_i ≤ 10⁹). The third line contains two integers a and b (0  ≤ b ≤  a ≤ 10⁹, a - b ≤ 10⁶).

Print a single integer — the required minimum number of moves needed to transform number a into number b.

3
3 4 5
30 17

6

3
5 6 7
1000 200

206