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:
def gcd(a,b):
    if b==0:
        return a
    return gcd(b,a%b)
def factor(n):
    a = []
    d = 2
    while d*d<=n:
        if n%d==0:
            a.append(d)
        d += 1
    if n>1:
        a.append(n)
    return a
def bs(lis,h):
    lo = 0
    hi = len(lis)-1
    while lo<=hi:
        mid = int((lo+hi)/2)
        if h>=lis[mid] and h<lis[mid+1]:
            return mid
        else:
            if h<=lis[mid]:
                hi = mid-1
            else:
                lo = mid+1
    return hi
a,b = map(int,raw_input().split())
n = int(raw_input())
a = gcd(a,b)
lis = factor(a)
for i in range(len(lis)):
    k = a/lis[i]
    if k*k != a:
        lis.append(k)
lis.sort()
for _ in range(n):
    ans =-1
    lo,hi = map(int,raw_input().split())
    if hi>=a:
        if lo>a:
            ans = -1
        else:
            ans = a
    else:
        c = bs(lis,hi)
        if lis[c] >= lo:
            ans = lis[c]
        else:
            ans = -1
    print ans