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=list(map(int,input().split()))
c=[]
for i in range(1,int(a**0.5)+1):
    if a%i==b%i==0:
        c.append(i)
    if b%(a//i)==a%(a//i)==0 and i!=a//i:
        c.append(a//i)
c.sort()
d=len(c)
for i in range(int(input())):
    e,h=list(map(int,input().split()))
    l,r=-1,d
    while r-l-1:
        m=(l+r)//2
        if c[m]>h:
            r=m
        else:
            l=m
    print(c[r-1] if h>=c[r-1]>=e else -1)