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 PYTHON):

Solution:
from __future__ import division
from sys import stdin, stdout
import math, bisect

def factor (x):
    lim = int (math.ceil (math.sqrt (x)))
    ans = set ()

    for i in xrange (1, lim + 1):
        if x % i == 0:
            ans.add (i)
            ans.add (x // i)
    
    return ans

A, B = map (int, stdin.readline ().split ())
set1, set2 = factor (A), factor (B)

shared = []

for i in set1:
    if i in set2:
        shared.append (i)

shared.sort ()

Q = int (stdin.readline ())

for q in xrange (Q):
    lo, hi = map (int, stdin.readline ().split ())
    idx = bisect.bisect_right (shared, hi)
    print shared[idx - 1] if idx and shared[idx - 1] >= lo else -1