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 bisect import bisect_left 
from math import *
def BinarySearch(a, x): 
    i = bisect_left(a, x) 
    if i: 
        return (i-1) 
    else: 
        return -1

a,b=map(int,input().split())
n=int(input())
ramu=gcd(a,b)
#print(ramu)
factors=set()
for i in range(1,int(ramu**0.5)+1):
    if(ramu%i==0):
        factors.add(i)
        factors.add(ramu//i)

factors=list(factors)

factors.sort()

#print(factors)

for i in range(n):
    low,high=map(int,input().split())
    res=BinarySearch(factors,high+1)
    
    res=factors[res]
    if(res<low):
        res=-1
    print(res)