Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Number Transformation II

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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*.

Input

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}).

Output

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

Examples

Input

3

3 4 5

30 17

Output

6

Input

3

5 6 7

1000 200

Output

206

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/14/2019 00:52:56 (f3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|