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 math import *

def gcdmax(x,y,T,S):
    bottom=0
    top=len(S)-1
    output=-1
    while bottom<=top:
        mid=(bottom+top)//2
        if T[mid]<x:
            bottom=mid+1
        elif T[mid]>y:
            top=mid-1
        else:
            output=max(output,T[mid])
            bottom=mid+1
    return(output)

def main():
    a,b=map(int,input().split())
    n=int(input())
    G=list()
    g=gcd(a,b)
    for i in range(1,int(sqrt(g))+1):
        if g%i==0:
            G.append(i)
            G.append(g//i)
    setG=set(G)
    G=list(setG)
    G.sort()
    for i in range(n):
        x,y=map(int,input().split())
        print(gcdmax(x,y,G,setG))
    
main()