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:
from math import gcd
from bisect import bisect
from functools import reduce
def factors(n):
    k = sorted(list(set(reduce(list.__add__,
                     ([i,n//i] for i in range(1,int(n**0.5+1)) if n%i == 0)))))
    return k
a,b = map(int,input().split())
gg = gcd(a,b)
f = factors(gg)
n = int(input())
for _ in range(0,n):
    l,h = map(int,input().split())
    ss = bisect(f,h)
    sss = f[ss-1]
    if sss < l:
        print(-1)
    else:
        print(sss)