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
import bisect
a,b=list(map(int,input().split()))
meragcd=math.gcd(a,b)


ans=[]
p=math.sqrt(meragcd)

#print(meragcd)
for i in range(2,int(p)+1):
    g=0
    if meragcd%i==0:
        if meragcd%i==i:
            ans.append(i)
        else:
            ans.append(i)
            ans.append(meragcd//i)
    
        
        
if meragcd>1:
    ans.append(meragcd)
ans=set(ans)
ans=list(ans)
ans.sort()
if 1 not in ans:
    ans.insert(0,1)
    
q=int(input())
for i in range(q):
    low,high=list(map(int,input().split()))
    index1=bisect.bisect_left(ans,low)
    index2=bisect.bisect_right(ans,high)
    if index1==len(ans):
        print(-1)
    elif (index2==index1) and index1!=len(ans) and index2!=len(ans):
        print(-1)
    else:
        print(ans[index2-1])