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 functools import reduce
import io,os,sys,math
def binarySearchkeeb(data,target,low,high):
    if low > high:
        return high
    else:
        mid=(low+high)//2
        if data[mid] <=target:
            return binarySearchkeeb(data,target,mid+1,high)
        else:
            return binarySearchkeeb(data,target,low,mid-1)
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def gcd(x,y):return math.gcd(x,y)
def allFactors(n):
    return set(reduce(list.__add__,
                ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
a,b=map(int,input().split())
re=sorted(allFactors(gcd(a,b)))
for _ in range(int(input())):
    l,h=map(int,input().split())
    ans=binarySearchkeeb(re,h,0,len(re)-1)
    if ans == -1:
        print(-1)
    else:
        c=re[ans]
        if l <= c:
            print(c)
        else:
            print(-1)