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
import bisect
input=stdin.readline
a,b=map(int,input().split())
p=set()
for i in range(1,int(a**0.5)+1):
  if a%i==0:
    if b%i==0:
      p.add(i)
    if b%(a//i)==0:
      p.add(a//i)
for i in range(1,int(b**0.5)+1):
  if b%i==0:
    if a%i==0:
      p.add(i)
    if a%(b//i)==0:
      p.add(b//i)
p=sorted(list(p))
p.sort()
n=int(input())
for _ in range(n):
  l,r=map(int,input().split())
  idx1=bisect.bisect_left(p,l)
  idx2=bisect.bisect_left(p,r)
  ans=-1
  for j in range(idx2-2,idx2+2):
    if 0<=j<len(p) and l<=p[j]<=r:
      ans=p[j]
  print(ans)