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 math,bisect

def factors(n):
    facts = set()
    for i in range(1,int(n**0.5)+1):
        if n%i == 0:
            facts.add(i)
            facts.add(n//i)

    facts = sorted(list(facts))

    return facts

def check(index,low,facts):
    if facts[index] < low:
        return False

    return True

def solve(facts,low,high,ans):
    index = bisect.bisect(facts,low)
    if index > 0 and facts[index-1] == low:
        index -= 1

    #print(index,facts)
    if index == len(facts):
        ans.append(-1)
        return
   
    index2 = bisect.bisect(facts,high)-1
    if low <= facts[index2] <= high:
        ans.append(facts[index2])
    else:
        ans.append(-1)
    

def main():
    a,b = map(int,input().split())
    g = math.gcd(max(a,b),min(a,b))
    facts = factors(g)
    q = int(input())
    ans = []
    for i in range(q):
        low,high = map(int,input().split())
        solve(facts,low,high,ans)

    for i in ans:
        print(i)


main()