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 bisect import bisect_right
from math import gcd
def find_le(k, x):
    i = bisect_right(k, x)
    if i:
        return i-1
a, b = map(int, input().split())
n = int(input())
g = gcd(a, b)
array = []
quantity = int(g**0.5)
for i in range(1, quantity + 1):
    if g%i == 0:
        array.append(i)
        array.append(g//i)
array.sort()
s = len(array)
for i in range(n):
    l, r = map(int, input().split())
    c = find_le(array, r)
    print(array[c] if array[c] >= l else -1)