A8128 | Modified GCD

Well, here is another math class task. In mathematics, GCD is the greatest common divisor, and it's an easy task to calculate the GCD between two positive integers.

A common divisor for two positive numbers is a number which both numbers are divisible by.

But your teacher wants to give you a harder task, in this task you have to 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. $low<=d<=high$ . 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.

The first line contains two integers $a$ and $b$ , the two integers as described above ( $1<=a,b<=10^{9}$ ). The second line contains one integer $n$ , the number of queries ( $1<=n<=10^{4}$ ). Then $n$ lines follow, each line contains one query consisting of two integers, $low$ and $high$ ( $1<=low<=high<=10^{9}$ ).

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