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:
def gcd(m, n):
	while n != 0:
		t = m % n
		m = n
		n = t

	return m


def get_divisors(g):
	from math import sqrt
	
	rt = int(sqrt(g))
	divisors = []

	for x in range(1, rt+1):
		if g % x == 0:
			divisors.append(x)
			divisors.append(g // x)

	if divisors[-1] ==  divisors[-2]:
		divisors.pop()

	divisors.sort()

	return divisors


def main():
	from sys import stdin, stdout
	from bisect import bisect_right

	# stdin = open("input.txt", "r")

	it = iter(map(int, stdin.read().split()))

	a, b = next(it), next(it)
	divisors = get_divisors(gcd(a, b))

	n = next(it)
	ans = []

	for _ in range(n):
		low, high = next(it), next(it)
		
		idx = bisect_right(divisors, high)
		d = divisors[idx-1]

		ans.append(str(d if low <= d <= high else -1))
		ans.append('\n')

	stdout.write(''.join(ans))


if __name__ == '__main__':
	main()