You are given a function that is similar to the Fibonacci series.

The function \(f\) is represented as follows: 

\(f(1)=a,f(2)=b,f(i)=f(i-1)+f(i-2)\) for integer \(i\geq 3\)

You do not know the numbers that are available in the sequence. You are also given \(q\) queries. Each query contains a number \(x\). Your task is to determine whether a positive \(i^{th}\) integer satisfies \(f(i)=x\).

Input format

• First line: Two integers \(a,\ b\) (\(0\leq a,b\leq 10^{18}\))
• Second line: An integer \(q\) (\(0\leq q\leq 10^6\))
• Each of the \(q\) lines: An integer \(x_i\) (\(0\leq x_i\leq 10^{18}\))

Output format

Print the answer for each of the \(q\) queries in a new line. Therefore, the output must contain q lines. Print \(YES\) if there is an integer that satisfies the condition. Otherwise, print \(NO\).