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 sys import stdin,stdout
import bisect as bs
nmbr = lambda: int(stdin.readline())
lst = lambda: list(map(int, input().split()))

for i in range(1):#nmbr():
    n1,n2=lst()
    d={}
    p=1
    while p*p<=n1:
        if n1%p==0:
            if p==n1//p:
                d[p]=d.get(p,0)+1
            else:
                d[p]=d.get(p,0)+1
                d[(n1//p)]=d.get(n1//p,0)+1
        p+=1
    p = 1
    while p * p <= n2:
        if n2 % p == 0:
            if p == n2 // p:
                d[p] = d.get(p, 0) - 1
            else:
                d[p] = d.get(p, 0) - 1
                d[(n2 // p)] = d.get(n2 // p, 0) - 1
        p+=1
    a=[]
    for k,v in d.items():
        if v==0:a+=[k]
    a.sort()
    ln=len(a)
    # print(a)
    for i in range(nmbr()):
        l,r=lst()
        p1=bs.bisect_left(a,l)
        p2=bs.bisect_left(a,r)
        if p2>=ln or a[p2]!=r:p2-=1
        if p1<=p2:print(a[p2])
        else:print(-1)