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:
from fractions import gcd
a,b = map(int, raw_input().split())
g = gcd(a, b)
c = []
for i in xrange(1,g+1):
    if i*i > g: break
    if g%i == 0:
        c.append(i)
        c.append(g/i)
c = sorted(c, reverse = True)
D = {}
for i in xrange(input()):
    l,r = map(int, raw_input().split())
    if D.has_key((l,r)):
        print D[(l,r)]
        continue
    for x in c:
        if l <= x <= r:
            D[(l,r)] = x
            print x
            break
    else:
        D[(l,r)] = -1
        print -1