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
from array import array  # noqa: F401
from math import gcd
from bisect import bisect_right


def input():
    return sys.stdin.buffer.readline().decode('utf-8')


a, b = map(int, input().split())
g = gcd(a, b)
divisors = [0]
d = 1
while d * d <= g:
    if g % d == 0:
        divisors.append(d)
        if d != g // d:
            divisors.append(g // d)
    d += 1

divisors.sort()

n = int(input())
ans = [-1] * n

for i, (low, high) in enumerate(map(int, input().split()) for _ in range(n)):
    j = bisect_right(divisors, high)
    if low <= divisors[j - 1] <= high:
        ans[i] = divisors[j - 1]

print(*ans, sep='\n')