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
r,o=map(int,input().split())
from bisect import *
def fact(x):
    ans=[]
    for  i in range(1,int(math.sqrt(int(x)))+1):
        if(x%i==0):
            if(x//i==i):
                ans.append(i)
            else:
                ans.append(x//i)
                ans.append(i)
    return ans;
m=int(input())
a=math.gcd(r,o)
tem=fact(a)
tem.sort()
for i in range(m):
    x,y=map(int,input().split())
    r=bisect_left(tem,y)
    if(r==len(tem)):
        if(tem[-1]<x):
            print(-1)
        else:
            print(tem[-1])
    else:
        if(tem[r]<=y):
            if(tem[r]<x):
                print(-1)
            else:
                print(tem[r])
        else:
            if(r==0):
                print(-1)
            else:
                if(tem[r-1]<x):
                    print(-1)
                else:
                    print(tem[r-1])