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:
from math import sqrt, gcd
import bisect


def commDiv(a, b):
    n = gcd(a, b)
    result = []
    for i in range(1, int(sqrt(n)) + 1):
        if n % i == 0:
            if n / i == i:
                result.append(i)
            else:
                result.append(i)
                result.append(n // i)

    return sorted(result)


if __name__ == "__main__":
    a, b = map(int, input().split())
    res = commDiv(a, b)
    q = int(input())
    # print('index', list(range(len(res))))
    # print('res', res)
    for _ in range(q):
        l, r = map(int, input().split())
        l_index = bisect.bisect_left(res, l)
        if (0 <= l_index < len(res)) and res[l_index] < l:
            l_index += 1

        r_index = bisect.bisect_left(res, r)
        if (0 <= r_index < len(res)) and res[r_index] > r:
            r_index -= 1

        # print(l, r)
        # print('l_index, r_index', l_index, r_index)
        # print('-------------')
        if l_index > r_index:
            print(-1)
        elif not (0 <= r_index < len(res)) and not (0 <= l_index < len(res)):
            print(-1)
        elif r_index >= len(res):
            print(res[-1])
        elif 0 <= r_index < len(res):
            print(res[r_index])
        elif 0 <= l_index < len(res):
            print(res[l_index])
        else:
            print(-1)
        # print('-------------')