A continued fraction of height n is a fraction of form $a_{1} + \frac{1}{a_{2} + \frac{1}{\ldots + \frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] 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 $2 + \frac{1}{4} = \frac{9}{4}$.

In the second sample $2 + \frac{1}{3 + \frac{1}{1}} = 2 + \frac{1}{4} = \frac{9}{4}$.

In the third sample $1 + \frac{1}{2 + \frac{1}{4}} = \frac{13}{9}$.