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():
    A, B = map( int, input().split())
    if A > B:
        A, B = B, A
    divisors = set()
    div = 1
    while div * div <= A:
        if A % div == 0:
            x = div
            y = A // div
            if B % x == 0:
                divisors.add(x)
            if B % y == 0:
                divisors.add(y)
        div = div + 1
    Q = int(input())
    divs = list(divisors)
    divs.sort()
    for i in range(0, Q):
        low, high = map( int, input().split())
        s, e, mid, sol = 0, len(divs) - 1, 0, -1
        while(s <= e):
            mid = s + (e - s) // 2
            if divs[mid] <= high:
                sol = mid
                s = mid + 1
            else:
                e = mid - 1
        if(divs[sol] < low):
            print(-1)
        else:
            print(divs[sol])

if __name__ == "__main__":
    main()