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
from sys import stdout

def print_fast(string):
    stdout.write(string + '\n')


def MGCD(_gcd, low, high):
    answer = -1
    botton = low
    index = min(_gcd, high)
    while index >= botton:
        if _gcd % index == 0:
            return  index
        index -= 1
    return answer


_input = input().split()
a = int(_input[0])
b = int(_input[1])

_gcd = math.gcd(a, b)

divisors = []

i = 1
while i * i <= _gcd:
    if _gcd % i == 0:
        divisors.append(i) 
        divisors.append(_gcd // i)
    i += 1

divisors = sorted(divisors)


testCases = int(input())

ans = []
for i in range(testCases):
    _input = input().split()
    l = int(_input[0])
    h = int(_input[1])
    answer = -1
    for i in divisors:
        if i > h:
            break
        if i >= l and i <= h:
            answer = i

    ans.append(str(answer))
    #ans.append(str(MGCD(_gcd, l, h)))

print_fast('\n'.join(ans))