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 array

def gcd(n,m):
    if m == 0:
        return n
    else:
        return gcd(m, n%m)

l = raw_input().split()
a = int(l[0])
b = int(l[1])

g = gcd(a,b) if a>b else gcd(b,a)

divs = []
i = 1
while i*i<=g:
    if g%i == 0:
        divs.append(i)
        divs.append(g/i)
    i=i+1
    
divs.sort()

arr = array.array('l',divs)

n = int(raw_input())


for _ in range(n):
    [c,d]=[int(i) for i in raw_input().split()]
    x = 0
    y = len(arr)
    while y-x>1:
        z = (x+y)/2
        if arr[z] == d:
            x = z
            break
        elif arr[z] > d:
            y = z
        else:
            x = z
    if arr[x] >= c:
        print arr[x]
    else:
        print -1