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 bisect import bisect_right, bisect_left
from collections import Counter
from heapq import heappop, heappush
from itertools import accumulate

R = lambda: map(int, input().split())
mi, mx = R()
g = math.gcd(mi, mx)
res = []
for x in range(1, int(math.sqrt(g)) + 1):
    if g % x == 0:
        res.append(x)
        res.append(g // x)
res.sort()
for x in range(int(input())):
    l, r = R()
    i = bisect_right(res, r) - 1
    if l <= res[i] <= r:
        print(res[i])
    else:
        print(-1)