Modified GCD

Find the greatest common divisor $d$ between two integers $a$ and $b$ that is in a given range from $low$ to $high$ (inclusive), i.e. $low\le d\le high$. It is possible that there is no common divisor in the given range.

You will be given the two integers $a$ and $b$, then $n$ queries. Each query is a range from $low$ to $high$ and you have to answer each query.

Input

The first line contains two integers $a$ and $b(1\le a,b\le 10^9)$. The second line contains the number of queries $n(1\le n\le 10^4)$. Then $n$ lines follow, each line contains one query consisting of two integers $low$ and $high(1\le low\le high\le 10^9)$.

Output

Print $n$ lines. The $i$-th of them should contain the result of the $i$-th query. If there is no common divisor in the given range for the query, print $-1$.

Examples