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
#from queue import *
#import random
#sys.setrecursionlimit(int(1e6))
input = sys.stdin.readline
 
############ ---- USER DEFINED INPUT FUNCTIONS ---- ############
def inp():
    return(int(input()))
def inara():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return(map(int,input().split()))
################################################################
############ ---- THE ACTUAL CODE STARTS BELOW ---- ############

a,b=invr()
g=math.gcd(a,b)
fact=[]
limit=int(math.sqrt(g+1))+1
for i in range(1,limit):
	if g%i==0:
		fact.append(i)
		if i*i!=g:
			fact.append(g//i)
fact.sort()
q=inp()
n=len(fact)
for _ in range(q):
	l,r=invr()
	hi=n-1
	lo=0
	ans=-1
	while hi>=lo:
		mid=(hi+lo)//2
		
		if (fact[mid]>=l) and (fact[mid]<=r):
			ans=fact[mid]
			lo=mid+1
		elif fact[mid]<l:
			lo=mid+1
		else:
			hi=mid-1
	print(ans)