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
# sys.stdin  = open("input.in","r")
from sys import stdin
input = stdin.readline
from heapq import heapify,heappush,heappop,heappushpop
from collections import defaultdict as dd, deque as dq,Counter as C
from math import factorial as f ,ceil,gcd,sqrt,log
from bisect import bisect_left as bl ,bisect_right as br
from itertools import combinations as c,permutations as p
from math import factorial as f ,ceil,gcd,sqrt,log
mp = lambda : map(int,input().split())
it = lambda: int(input())
ls = lambda : list(input().strip())
def isprime(n):
	for j in range(3,int(sqrt(n))+1,2):
		if n%j==0:
			return 0
	return 1
def factors(n):
	s = set()
	s.add(1)
	s.add(n)
	for j in range(2,int(sqrt(n))+1):
		if n%j==0:
			s.add(j)
			s.add(n//j)
	return s
a,b = mp()
k = sorted(factors(a))
for _ in range(it()):
	l,h = mp()
	ans =-1
	for el in range(br(k,h)-1 ,bl(k,l)-1,-1):
		if b%k[el]==0:
			ans = k[el]
			break
	if ans>=l and ans<=h:
		print(ans)
	else:
		print(-1)