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 PYTHON3):

Solution:
def main():
    from math import gcd,sqrt
    from bisect import bisect
    a, b = map(int, input().split())
    divisors, x = [1], gcd(a, b)
    p = q = 1
    divisors = [1]
    while not x % 2:
        x //= 2
        p *= 2
        divisors.append(p)
    l = []
    while not x % 3:
        x //= 3
        q *= 3
        l.append(q)
    divisors += [p * q for p in l for q in divisors]
    lim = int(sqrt(x))
    for p in -1, 1:
        while True:
            if p >= lim:
                break
            for p in range(p + 6, lim + 6, 6):
                if not x % p:
                    l, q = [], 1
                    while not x % p:
                        x //= p
                        q *= p
                        l.append(q)
                    divisors += [p * q for p in l for q in divisors]
                    lim = int(sqrt(x))
                    break
            else:
                break
    if x != 1:
        divisors += [x * q for q in divisors]
    divisors.sort()
    res = []
    for _ in range(int(input())):
        lo, hi = map(int, input().split())
        d = divisors[bisect(divisors, hi) - 1]
        res.append(d if lo <= d else -1)
    print('\n'.join(map(str, res)))


if __name__ == '__main__':
    main()