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:
I = lambda : map(int,input().split())
import bisect as bi
def div(s):
    s=int(s)
    l=set([1,s])
    for i in range(2,int(s**0.5)+1):
        if s%i==0:
            l.add(s//i)
            l.add(i)
    return l
p,q = map(div,input().split());a=p&q
p=sorted(a)
for _ in range(int(input())):
    a,b = I()
    t=bi.bisect(p,b)
    #print(t,p)
    x = p[t-1] if (t-1<len(p) and p[t-1]>= a) else -1
    print(x)