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 sys,math as mt,bisect as bi
input = sys.stdin.readline
I = lambda : list(map(int,input().split()))

a,b=I()
q,=I()
p=mt.gcd(a,b)
an=[1,p]
i=2
while i*i<=p:
	if p%i==0:
		an.append(i)
		if i!=p//i:
			an.append(p//i)
	i+=1
an.sort()
for _ in range(q):
	l,r=I()
	x,y=bi.bisect(an,l),bi.bisect(an,r)
	a,b=an[x-1],an[y-1]
	#print(b,x)
	if l<=b<=r:
		print(b)
	else:
		print(-1)