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:
"""
Code of Ayush Tiwari
Codeforces: servermonk
Codechef: ayush572000

"""
import sys
import math
from bisect import bisect_right
input = sys.stdin.buffer.readline
def solution():
    n,m=map(int,input().split())
    x=math.gcd(n,m)
    l=[]
    for i in range(1,int(x**0.5)+1):
        if x%i==0:
            if x//i==i:
                l.append(i)
            else:
                l.append(i)
                l.append(x//i)
    l.sort()
    for _ in range(int(input())):
        a,b=map(int,input().split())    
        x=bisect_right(l,b)
        if l[x-1]<a:
            print(-1)
        else:
            print(l[x-1])


solution()