A continued fraction of height n is a fraction of form $\text{[math]}$ . You are given two rational numbers, one is represented as $\text{[math]}$ 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 ≤ 10¹⁸) — 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 a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10¹⁸) — 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.

Note

In the first sample $\text{[math]}$ .

In the second sample $\text{[math]}$ .

In the third sample $\text{[math]}$ .

Continued Fractions

Examples