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 bisect

def gcd(a, b):
    while b > 0:
        t = b
        b = a % b
        a = t
    return a


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

g = gcd(a, b)
d = []

i = 1
while i*i < g:
    if g % i == 0:
        d.append(i)
        d.append(g // i)
    i += 1

if i*i == g:
    d.append(i)

d.sort()

n = int(input())

for i in range(0, n):
    low, high = map(int, input().split())
    r, l = bisect.bisect_right(d, high), bisect.bisect_left(d, low)
    if r > l:
        print(d[r - 1])
    else:
        print(-1)