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 collections import Counter
from bisect import bisect_right as br

saved = {}


def gcd(a, b):
    return a if b == 0 else gcd(b, a % b)


def pf(num):
    i = 2
    ps = []

    while num > 1:
        if num % i == 0:
            num //= i
            ps.append(i)
        else:
            i += 1

    return ps


# all the factors of a number in sqrt(n) time
def f(num):
    i = 1
    res = []
    while i * i <= num:
        if num % i == 0:
            res.append(num // i)
            if i != num // i:
                res.append(i)
        i += 1
    return sorted(res)


# O(n^1.5) tle at 1:30 p.m. 5-1-15
def solve(c, x, y):
    for i in range(y, x-1, -1):
        if i in saved and saved[i] != -1:
            return i

        if not Counter(pf(i)) - Counter(c):
            return i
        else:
            saved[i] = -1

    return -1


def solve1(c, x, y):
    res = c[br(c, y)-1]
    return res if res >= x else -1

if __name__ == "__main__":
    args = map(int, input().split())
    n1, n2 = args
    g = f(gcd(n1, n2))

    for _ in range(int(input())):
        r1, r2 = map(int, input().split())
        print(solve1(g, r1, r2))