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:
from bisect import bisect_left, bisect_right, insort
import sys
import heapq
from math import *
from collections import defaultdict as dd
from collections import deque
def data(): return sys.stdin.readline().strip()
def mdata(): return map(int, data().split())

a,b=mdata()
div=[]
a,b=min(a,b),max(a,b)
for i in range(1,int(a**0.5)+1):
    if a%i==0:
        if b%i==0:
            div.append(i)
        if b%(a//i)==0 and i!=a//i:
            div.append(a//i)
div.sort()
n=int(input())
for i in range(n):
    a,b=mdata()
    b1=bisect_right(div,b)
    a1=bisect_left(div,a)
    if b1-a1==0:
        print(-1)
    else:
        print(div[b1-1])