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:
import math

def main():
    (a,b) = list(map(int,input().split()))
    if b > a:
        a, b = b, a
    while b != 0:
        b, a = a%b, b
    divisors = []
    root = math.floor(math.sqrt(a))
    for divisor in range(1,root):
        if a % divisor == 0:
            divisors.append(divisor)
            divisors.append(a//divisor)
    if a % root == 0:
        divisors.append(root)
        if root**2 != a:
            divisors.append(a//root)
    divisors.sort()
    divisors = [0] + divisors
    length = len(divisors)
    n = int(input())
    for _ in range(n):
        (low,high) = list(map(int, input().split()))
        left = 1
        right = length
        best = 0
        while left < right:
            middle = (left+right)//2
            if divisors[middle] > high:
                right = middle
            else:
                best = divisors[middle]
                left = middle + 1
        if best < low:
            print("-1")
        else:
            print(best)        
    
main()