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 bisect
def gcd(a, b):
  while a != 0:
    a, b = b % a, a
  return b
 
def calc_divisors(num):
  divisors = []
  for i in range(1, int(math.sqrt(num)) + 1):
    n, f = divmod(num, i)
    if f == 0:
      divisors.append(i)
      divisors.append(n)
  divisors.sort()
  return divisors
 
a, b = map(int, input().split())
common_divisors = calc_divisors(gcd(a, b))
 
size = int(input())
result = ['-1'] * size
for i in range(size):
  low, high = map(int, input().split())
  ie = bisect.bisect_right(common_divisors, high)
  cd = common_divisors[ie - 1]
  if (low <= cd <= high):
    result[i] = str(cd)
 
print('\n'.join(result))