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:
def arr_inp(n):
    if n == 1:
        return [int(x) for x in stdin.readline().split()]
    elif n == 2:
        return [float(x) for x in stdin.readline().split()]
    else:
        return [str(x) for x in stdin.readline().split()]


def factorize(n):  # o(sqr(n))
    c, ans = 1, []
    while (c * c < n):
        if n % c == 0:
            ans.extend([c, n // c])
        c += 1

    if c * c == n:
        ans.append(c)
    return sorted(ans)


from sys import stdin
from math import gcd
from bisect import *

a, b = arr_inp(1)
arr = factorize(gcd(a, b))
# print(arr)

for i in range(int(input())):
    lo, hi = arr_inp(1)
    if hi < arr[0] or lo > arr[-1]:
        print(-1)
    else:
        ixh = bisect_right(arr, hi)
        if ixh == len(arr):
            print(arr[ixh - 1])
        elif ixh > 0 and arr[ixh] > hi and arr[ixh - 1] < lo:
            print(-1)
        elif arr[ixh] == hi:
            print(arr[ixh])
        else:
            print(arr[ixh - 1])