A9071 | Number Transformation II

You are given a sequence of positive integers $x_{1},x_{2},...,x_{n}$ 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 $n$ ( $1<=n<=10^{5}$ ). The second line contains $n$ space-separated integers $x_{1},x_{2},...,x_{n}$ ( $2<=x_{i}<=10^{9}$ ). The third line contains two integers $a$ and $b$ ( $0<=b<=a<=10^{9}$ , $a-b<=10^{6}$ ).

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