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:
import math;
import bisect;
from bisect import bisect_left;

line = raw_input().split(' ');
a = int (line[0]);
b = int (line[1]);

divs_a = [];
divs_b = [];


#Get Divisors of A
for i in range (1, int(math.sqrt(a))+1):
    if a%i==0:
        divs_a.append(i);
        if i!=a/i:
            divs_a.append(a/i);


#Get Divisors of B
for i in range (1, int(math.sqrt(b))+1):
    if b%i==0:
        divs_b.append(i);
        if i != b/i:
            divs_b.append(b/i);

divs_a = sorted(divs_a);
divs_b = sorted(divs_b);

#Get intersection
divs_intersect = [val for val in divs_a if val in divs_b];

#print divs_a;
#print divs_b;
#print divs_intersect;

queries = int (raw_input());

for j in range (queries):
    line = raw_input().split(' ');
    low = int (line[0]);
    hi = int (line[1]);
    ind = bisect.bisect_left(divs_intersect, hi);

    #process
    if ind==len(divs_intersect):
        ind = ind - 1;
        if ind>=0:
            if divs_intersect[ind]>=low:
                print divs_intersect[ind];
            else:
                print -1;
                
        else:
            print -1;

    else:
        if ind<0:
            print -1;
        elif divs_intersect[ind]==hi:
            print hi;
        else:
            ind = ind-1;
            if ind>=0:
                if divs_intersect[ind]>=low:
                    print divs_intersect[ind];
                else:
                    print -1;

            else:
                print -1;