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 sys,math as mt
import heapq as hp
import collections as cc
import math as mt
import itertools as it
import bisect as bi
input=sys.stdin.readline
I=lambda:list(map(int,input().split()))
sys.setrecursionlimit(8*10**5)
a,b=I()
g=mt.gcd(a,b)
div=set()
for i in range(2,int(g**0.5)+1):
	if g%i==0:
		div.add(i)
		div.add(g//i)
div=[1]+list(div)+[g]
div.sort()
for tc in range(int(input())):
	x,y=I()
	tf=0
	temp=bi.bisect_right(div,y)
	if x<=div[temp-1] and div[temp-1]<=y:
		print(div[temp-1])
	else:
		print(-1)