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:
import math
a,b=input().split()
a,b=[int(a),int(b)]
n=int(input())
g=math.gcd(a,b)
ar=[]
i=1
while i*i<=g:
    if g%i==0:
        ar.append(i)
        ar.append(g//i)
    i+=1
ar.sort(reverse=True)
for i in range(0,n):
    c,d=input().split()
    c,d=[int(c),int(d)]
    i=0
    flag=0
    if c==d:
        if a%c==0 and b%c==0:
            print(c)
        else:
            print("-1")
    else:
        while i < len(ar):
            if ar[i] >= c and ar[i] <= d:
                flag = 1
                break
            i += 1
        if flag == 1:
            print(ar[i])
        else:
            print("-1")