Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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C. Modified GCD

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWell, 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.

Input

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}).

Output

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.

Examples

Input

9 27

3

1 5

10 11

9 11

Output

3

-1

9

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