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 math import sqrt
import bisect

def gcd(a,b):
    if b == 0:
        return a
    else :
        return gcd(b,a%b)
        
def create_divlist(gg):
    tmp = [-1]
    for x in xrange(1,int(sqrt(gg)+1)):
        if gg%x == 0:
            tmp.append(x)
            tmp.append(gg/x)
    return sorted(tmp)
    
a,b = map(int,raw_input().split())
n = int(raw_input())
gg = gcd(a,b)
divset = create_divlist(gg)

for x in xrange(n):
    i,j = map(int,raw_input().split())
    k = bisect.bisect_right(divset,j)
    print divset[k-1] if k and divset[k-1]>=i else "-1"