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:
from sys import stdin
from math import gcd
from bisect import bisect
input = stdin.readline
a,b = map(int, input().split())
g = gcd(a, b)

f = []
for i in range(1, int(g ** 0.5) + 1):
	if g % i == 0:
		f.append(i)
		if g // i != i:
			f.append(g // i)
f.sort()
for _ in range(int(input())):
	l, h = map(int, input().split())
	if l <= g <= h:
		print(g)
		continue
	if l > g:
		print(-1)
		continue
	if h < g:
		i = bisect(f,h)
		if f[i-1] >= l:
			print(f[i-1])
		else:
			print(-1)