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,sys
from collections import Counter, defaultdict, deque
from sys import stdin, stdout
input = stdin.readline
li = lambda:list(map(int,input().split()))

def factors(g):
    fact=[]
    for i in range(1,int(math.sqrt(g))+1):
        if(g%i==0):
            if(i*i==g):
                fact.append(i)
            else:
                fact.append(i)
                fact.append(g//i)
    fact.sort(reverse=True)
   # print(*fact)
    return(fact)

def case():
    a,b=li()
    g=math.gcd(a,b)
   # print(g)
    fact=factors(g)
    q=int(input())
    for i in range(q):
        l,r=li()
        flag=0
        for j in range(len(fact)):
            if(fact[j]<=r and fact[j]>=l):
                print(fact[j])
                flag=1
                break
        if(not flag):
            print(-1)


for _ in range(1):
    case()