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
def m_divlist(n):
    tmp = [-1]
    for x in range(1,int(n**0.5+1)):
        if (n%x) == 0:
            tmp.append(x)
            tmp.append(int(n/x))
    tmp.sort()
    return tmp

a0,b0=map(int,input().split(' '))
a=a0;b=b0

while a!=0 and b!=0:
    if a > b: a = a % b
    else: b = b % a
mcd=a+b

mdvlst=m_divlist(mcd)
n=int(input())
for i in range(n):
    rmin,rmax=map(int,input().split(' '))
    k = bisect.bisect(mdvlst,rmax)
    print (mdvlst[k-1] if mdvlst[k-1]>=rmin else '-1')