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
def bs(x, y, p):
	l, r=0, len(p)-1
	z=-1
	while l<=r:
		m=(l+r)//2
		if x<=p[m]<=y:
			z=p[m]
			l=m+1
		elif p[m]>y:
			r=m-1
		else:
			l=m+1
	return z
a, b=map(int, input().split())
g=math.gcd(a, b)
s=int(math.sqrt(g))+1
p=[]
for i in range(1, s):
	if not g%i:
		p.append(i)
l=len(p)-1
l-=(s-1)*(s-1)==g
for i in range(l, -1, -1):
	p.append(g//p[i])
for _ in range(int(input())):
	x, y=map(int, input().split())
	print(bs(x, y, p))