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:
from math import gcd
x,y=map(int,input().split())
g=gcd(x,y)
div=[]
for i in range(1,int(g**0.5)+1):
    if g%i==0:
        if i*i==g:
            div.append(i)
            break
        else:
            div.append(i)
            div.append(g//i)
div.sort()
for q in range(int(input())):
    ans=-1
    l,r=map(int,input().split())
    lo,hi=0,len(div)-1
    while(lo<=hi):
        mid=(lo+hi)//2
        if div[mid]>r:
            hi=mid-1
        elif div[mid]<l:
            lo=mid+1
        else:
            ans=div[mid]
            lo=mid+1
    print(ans)