CF75C.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.

好吧，这里又是一道数学课的题目。在数学中，GCD（最大公约数）是指两个正整数的最大公因数，计算两个正整数的 GCD 是一个简单任务。

两个正整数的一个公因数，是指能同时整除这两个数的数。

但你的老师想给你一个更难的任务：在此任务中，你需要找出两个整数 $a$ 和 $b$ 的最大公约数 $d$，且该 $d$ 必须落在给定的区间 $[low, high]$ 内（即满足 $low \leq d \leq high$）。有可能在给定区间内不存在这样的公因数。

你将被给出两个整数 $a$ 和 $b$，然后是 $n$ 个查询。每个查询给出一个区间 $[low, high]$，你需要对每个查询作出回答。

The first line contains two integers a and b, the two integers as described above (1 ≤ a, b ≤ 109). The second line contains one integer n, the number of queries (1 ≤ n ≤ 104). Then n lines follow, each line contains one query consisting of two integers, low and high (1 ≤ low ≤ high ≤ 109).

第一行包含两个整数 $a$ 和 $b$，即上述描述的两个整数（$1 \le a, b \le 10^9$）。第二行包含一个整数 $n$，表示查询次数（$1 \le n \le 10^4$）。随后是 $n$ 行，每行包含一个查询，由两个整数 $low$ 和 $high$ 组成（$1 \le low \le high \le 10^9$）。

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.

输出 n 行。其中第 i 行应包含输入中第 i 个查询的结果。若某个查询在给定范围内不存在公共因数，则该查询的结果应输出 -1。