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 PYTHON3):

Solution:
a,b = map (int ,input().split())
n = int (input())
def gcd(a,b):
    if (b == 0):
         return a
    return gcd(b, a % b);
def bs (l,r,val,a):
    l1 = l
    r1 = r
    res = 0 ;
    while (l1 <= r1 ):
        mid= (l1+r1)// 2
        if (a[mid] <= val):
            l1 = mid +1 ;
            res =a[mid]
        else :
            r1 = mid-1
    return res
t= gcd (a,b)
wish  = [] # list of root store here
for i in range (1,t+1):
    if  t// i   < i :
        break ;
    if t%i == 0 :
        wish.append (i)
        if (t // i != i):
            wish.append(t//i)
wish.sort()
for i in range (0,n):
    low,high = map (int,input().split())
    temp = bs (0,len(wish)-1,high,wish)
    if temp < low:
        temp = -1 ;
    print (temp)