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 PYTHON):

Solution:
s = raw_input().split()
a = int(s[0])
b = int(s[1])
while True:
	if b == 0:
		break
	a %= b
	if a == 0:
		break
	b %= a
gcd = a+b

i = 1
q = []
while i*i <= gcd:
	if gcd % i == 0:
		q.append(i)
		q.append(gcd/i)
	i += 1
q.sort()
q.reverse()

c = int(raw_input())
while c > 0:
	c -= 1
	s = raw_input().split()
	a = int(s[0])
	b = int(s[1])
	x = -1
	for i in q:
		if i <= b:
			if i >= a:
				x = i
			break
	print x