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
import bisect

def calc_divisors(a, b):
    a, b = (a, b) if a < b else (b, a)
    divisors = []
    for i in range(1, int(math.sqrt(a)) + 1):
        an, af = divmod(a, i)
        bn, bf = divmod(b, i)
        if af == bf == 0:
            divisors.append(i)
        if b % an == af == 0:
            divisors.append(an)
    divisors.sort()
    return divisors

a, b = map(int, input().split())
common_divisors = calc_divisors(a, b)

size = int(input())
result = [0] * size
for i in range(size):
    low, high = map(int, input().split())
    ie = bisect.bisect_right(common_divisors, high)
    cd = common_divisors[ie - 1]
    result[i] = str(cd) if (low <= cd <= high) else '-1'

print('\n'.join(result))