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 fractions import gcd
from math import sqrt

d = []
ha = {}

def get_factors(a):
    se = set()
    for i in range(1, int(sqrt(a)) + 1):
        if a % i == 0:
            se.add(i)
            se.add(a // i)
    return se

def bsearch(l, h):
    if (l, h) in ha:
        return ha[(l, h)]
    global d
    for s in d:
        if s <= h and s >= l:
            ha[(l, h)] = s
            return s
    ha[(l, h)] = -1
    return -1

(a, b) = map(int, input().split(' '))

ad = get_factors(a)
bd = get_factors(b)
d = list(reversed(sorted(list(ad.intersection(bd)))))

n = int(input())

for i in range(n):
    (l, h) = map(int, input().split(' '))
    print(bsearch(l, h))