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A9028. Continued Fractions

编程题 普及/提高-

题目描述

A continued fraction of height $n$ is a fraction of form ![](/uploads/luogu/CF305B/19ade84928d3d628a6e212b03adbbf8bc0856736_47e6063ce9cd.png). You are given two rational numbers, one is represented as ![](/uploads/acgo/image/0a471916b15bd29d_03cadc3da1e0.jpeg) and the other one is represented as a finite fraction of height $n$ . Check if they are equal.

输入格式

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.

输出格式

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

输入输出样例

输入 #1
9 4
2
2 4
输出 #1
YES
输入 #2
9 4
3
2 3 1
输出 #2
YES
输入 #3
9 4
3
1 2 4
输出 #3
NO

说明/提示

In the first sample ![](/uploads/acgo/image/7ab0b5ef3eebe6bd_79d477ceace2.jpeg).

In the second sample ![](/uploads/acgo/image/5ae5022375e9e871_8d9eeff8f737.jpeg).

In the third sample ![](/uploads/acgo/image/8b3939a6ca77c2f5_1cbf4b742847.jpeg).
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