A 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.

Note

In the first sample .

In the second sample .

In the third sample .