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:
n,m = [int(i) for i in input().split()]
l = []
for i in range(1,int(n**0.5)+1):
	if n%i == 0 and m%i == 0:
		l.append(i)
	if n%(n//i) == 0 and m%(n//i) == 0:
		l.append(n//i)
l.sort()
n = int(input())
for i in range(n):
	q,w = [int(j) for j in input().split()]
	mx = -1
	for j in range(len(l)-1,-1,-1):
		if q<=l[j]<=w:
			mx = l[j]
			break
	print(mx)