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 math
import sys
def gcd(a, b):
  while b>0:
    rest = a%b
    a = b
    b = rest
  return a


dividers = []
(a, b) = tuple(map(int, input().split()))
cases = int(input())
g = gcd(a, b)
for x in range(1, int(math.sqrt(g)//1)+1):
  if g%x==0:
    dividers.append(x)
    dividers.append(g//x)
dividers.sort()
dividers = list(dict.fromkeys(dividers))
#print(dividers)
for x in range(cases):
  (low, high) = tuple(map(int, input().split()))
  ans = 0
  if dividers[0] == high:
    print(dividers[0])
    continue
  if low > dividers[-1] or high < dividers[0]:
    print('-1')
    continue
  elif dividers[-1] <= high and dividers[-1] >=low:
    print(dividers[-1])
    continue
  start = 0
  end = len(dividers)-1
  mid = (start+end+1)//2
  while start<end:
    mid = (start+end+1)//2
    if dividers[mid] > high:
      end = mid-1
    else:
      start = mid
    if dividers[mid] <= high and dividers[mid+1] > high:
      ans = dividers[start]
      break
    #else:
    #  ans = dividers[mid]
  ans = dividers[start]
  if ans >= low and ans <= high:
    print(ans)
  else:
    print('-1')