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
def gcd(a,b): 
    if(b==0): 
        return a 
    else: 
        return gcd(b,a%b) 
a,b=map(int,input().split())
q=int(input())
x=gcd(a,b)
l=[]
for i in range(1,int(math.sqrt(x))+1):
    if(x%i==0):
        if(i*i==x):
            l.append(i)
        else:
            l.append(i)
            l.append(x//i)
l.sort()
for _ in range(q):
    s,e=map(int,input().split())
    low=0;high=len(l)-1
    ans=-1
    #print(s,e)
    while(low<=high):
        
        mid=(low+high)//2
        
        if(l[mid]==e):
            ans=l[mid]
            break
        elif(l[mid]<e):
            ans=l[mid]
            low=mid+1
            
        else:
            high=mid-1

    if(ans==-1 or ans<s):
        print(-1)
    else:
        print(ans)