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 ACM-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

B. Continued Fractions

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA continued fraction of height *n* is a fraction of form . You are given two rational numbers, one is represented as and the other one is represented as a finite fraction of height *n*. Check if they are equal.

Input

The first line contains two space-separated integers *p*, *q* (1 ≤ *q* ≤ *p* ≤ 10^{18}) — the numerator and the denominator of the first fraction.

The second line contains integer *n* (1 ≤ *n* ≤ 90) — the height of the second fraction. The third line contains *n* space-separated integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{18}) — the continued fraction.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output

Print "YES" if these fractions are equal and "NO" otherwise.

Examples

Input

9 4

2

2 4

Output

YES

Input

9 4

3

2 3 1

Output

YES

Input

9 4

3

1 2 4

Output

NO

Note

In the first sample .

In the second sample .

In the third sample .

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/30/2017 23:19:42 (p1).

Desktop version, switch to mobile version.
User lists

Name |
---|