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
from collections import Counter


def read_int():
    return int(input().strip())


def read_ints():
    return list(map(int, input().strip().split(' ')))


def index(array, e):
    # find highest index i such that a[i] <= e < a[i+1]
    low, high = 0, len(array)-1
    # array: [1, 3, 9] e: 5
    while low < high:
        mid = (low+high+1)//2
        if e >= array[mid]:
            low = mid
        else:
            high = mid-1
    return low


def solve():
    a, b = read_ints()
    gcd = math.gcd(a, b)
    divisors, highs = [], []
    i = 2
    for i in range(1, int(math.sqrt(gcd)+1)):
        if gcd%i == 0:
            if i != gcd//i:
                divisors.append(i)
                highs.append(gcd//i)
            else:
                divisors.append(i)
    highs.reverse()
    divisors.extend(highs)
    n = read_int()
    for _ in range(n):
        low, high = read_ints()
        highest_divisor = divisors[index(divisors, high)]
        if highest_divisor >= low:
            print(highest_divisor)
        else:
            print(-1)


if __name__ == '__main__':
    solve()