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
import math 
  
def read_line():
	return sys.stdin.readline()[:-1]
 
def read_int():
	return int(sys.stdin.readline())
 
def read_int_line():
	return [int(v) for v in sys.stdin.readline().split()]

def printDivisors(n,ls) : 
	i = 1
	while i <= math.sqrt(n): 	  
		if (n % i == 0) : 
			if (n // i == i) : 
				ls.append(i) 
			else :  
				ls.append(i)
				ls.append(n//i) 
		i = i + 1
	return ls

def gcd(a,b):
	if b==0:
		return a
	else:
		return gcd(b,a%b)

def find(ls,l,h):
	if len(ls)==0:
		return -1
	else:
		x = len(ls)//2
		if l<=ls[x]<=h and x == len(ls)-1:
			return ls[x]
		elif l<=ls[x]<=h:
			if ls[x+1]>h:
				return ls[x]
			else:
				return find(ls[x:],l,h)
		elif ls[x]>=h:
			return find(ls[:x],l,h)
		else:
			return find(ls[x+1:],l,h)

a,b = read_int_line()
g = gcd(a,b)
ls = []
ls = printDivisors(g,ls)
ls.sort()
n =read_int()
l=[0]*n
h=[0]*n
for i in range(n):
	l[i],h[i] = read_int_line()

for i in range(n):
	print(find(ls,l[i],h[i]))