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 PYTHON):

Solution:


def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

def find(x):
    l = -1
    r = len(divs)
    while r - l > 1:
        mid = (l + r) / 2
        if divs[mid] <= x:
            l = mid
        else:
            r = mid
    return divs[l]

a, b = map(int, raw_input().split())
m = gcd(a, b)
divs = [1, m]
d = 2
while d * d < m:
    if m % d == 0:
        divs.append(d)
        divs.append(m / d)
    d += 1
if d * d == m:
    divs.append(d)
divs.sort()

q = input()
for _ in range(q):
    l, h = map(int, raw_input().split())
    resp = find(h)
    if resp >= l:
        print(resp)
    else:
        print(-1)