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 \le q \le p \le 1018) - the numerator and the denominator of the first fraction.The second line contains integer n (1 \le n \le 90) - the height of the second fraction. The third line contains n space-separated integers a1,a2,...,an (1 \le ai \le 1018) - the continued fraction.Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

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

In the first sample .In the second sample .In the third sample .