Problem: 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.

Input

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).

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

Solution (in PYTHON):

Solution:
__author__ = 'xywang'
import sys
from fractions import gcd
from bisect import bisect_right

class CodeForces:
    def get_result(self):
        n, m = map(int, sys.stdin.readline().split(" "))
        commonDivisor = list()
        i = 1
        g = gcd(n, m)
        while i * i <= g:
            if g % i == 0:
                commonDivisor.append(i)
                commonDivisor.append(g / i)
            i += 1
        commonDivisor.sort()
        n = int(sys.stdin.readline())
        for i in range(n):
            low, high = map(int, sys.stdin.readline().split(" "))
            k = commonDivisor[bisect_right(commonDivisor, high) - 1]
            print -1 if k < low else k




def main():
    code = CodeForces()
    code.get_result()

if __name__ == "__main__":
    main()