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:
''' Author @isumit '''
import math
def solve():
	A, B= map(int, input().split())
	gcdab = math.gcd(A, B)
	divisors = []
	i = 1
	while i*i <= gcdab:
		if gcdab % i == 0 :
			divisors.append(i)
			divisors.append(gcdab//i)
		i += 1
	divisors = sorted(divisors)
	for _ in range(int(input())):
		left, right = map(int, input().split())
		res = -1
		for i in divisors:
			if left <= i and i <= right:
				res = max(res, i)
		print(res)
Testcase = 1
#Testcase = int(input())
for _ in range(Testcase):
	solve()
''' https://codeforces.com/problemset/problem/75/C '''