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:
import math
def factorize(n):
	factors = []
	s = int(math.ceil(math.sqrt(n)))
	for i in xrange(1,s+1):
		if n%i==0:
			factors.append(i)
			if n/i != i :
				factors.append(n/i)
	factors.sort()
	return factors
def intersection(a,b):
	return list(set(a)&set(b))
#-------------------------------------------------------
a,b = map(int,raw_input().split())
n = int(raw_input())
low =[]
high=[]
divisor = intersection(factorize(a),factorize(b))
for i in xrange(n):
	a,b = map(int,raw_input().split())
	low.append(a)
	high.append(b)
for i in xrange(n):
	div_set = []
	for element in divisor:
		if element<=high[i] and element>=low[i]:
			div_set.append(element)
	if len(div_set)==0:
		print -1
	else:
		print max(div_set)