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 bisect
a,b=map(int,input().split())
def d(n):
    q=int(n**.5)+1
    r={1}
    for i in range(1,q):
        if n%i==0:r.add(i);r.add(n//i)
    return r
q=sorted(d(a)&d(b))
w=set(q)
for i in range(int(input())):
    k=-1
    l,h=map(int,input().split())
    o=bisect.bisect_right(q,h)
    if o-bisect.bisect_left(q,l)or h in w or l in w>1:k=q[o-1]
    print(k)