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
from sys import *
from bisect import bisect_right

input=stdin.readline
print=stdout.write

a,b=map(int,input().split())
n=int(input())

gcd=math.gcd(a,b)
##print(gcd)
factors=[]
i=1
while(i*i<=gcd):
    if gcd%i==0:
        factors.append(gcd//i)

        if (i*i)!=gcd:
            factors.append(gcd//(gcd//i))

    i+=1

factors.sort()

for _ in range(n):
    l,h=map(int,input().split())
    ans=-1
    index=bisect_right(factors,h)

    if factors[index-1]>=l and factors[index-1]<=h:
        ans=factors[index-1]
    
    print(str(ans)+'\n')