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 factors(n):
    i = 2
    res = list()
    while i*i <= n:
        if n % i == 0:
            cnt = 0
            while n % i == 0:
                n //= i
                cnt += 1
            res.append((i, cnt))

        i += 1
    if not n == 1:
        res.append((n, 1))
    return res


def generate_divisors(factors, ind, result, divisors):
    if ind == len(factors):
        divisors.append(result)
        return
    
    for i in range(factors[ind][1] + 1):
        generate_divisors(factors, ind+1, result, divisors)
        result *= factors[ind][0]
    
    if ind == 0:
        return divisors


def search(s, e, x, y):
    while s < e:
        mid = s + (e - s)//2
        if y >= common[mid]:
            s = mid + 1
        else:
            e = mid + 0
    return common[s-1]


a, b = map(int, input().strip().split())
div_a = generate_divisors(factors(a), 0, 1, [])
div_b = generate_divisors(factors(b), 0, 1, [])
common = list(set(div_a).intersection(set(div_b)))
common = sorted(common)
c_size = len(common)
c_max, c_min = common[c_size-1], common[0]
# print(factors(a))
# print(factors(b))
# print(common)
# print(c_max, c_min)

n = int(input())
for _ in range(n):
    x, y = map(int, input().strip().split())
    if x > c_max or y < c_min:
        print(-1)
    else:
        ans = search(0, c_size, x, y)
        if ans < x or ans > y:
            print(-1)
        else:
            print(ans)