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 JAVA):

Solution:
import java.util.*;
import java.io.*;
public class cf
{
    static long s;
    static long n;
    
    static int arr[];
    static int brr[];
    static int counter;
    static int l;
    static int r;
    public static int gcd(int a, int b)
    {
        if (a == 0) 
        return b;
        return gcd(b%a,a);
    }
    public static void commDiv(int a,int b)
    {
        int n = gcd(a, b);
        int result = 0;
        for (int i=1; i<=Math.sqrt(n); i++)
        {
            if (n%i==0)
            {
                if (n/i == i)
                arr[counter++]=i;
                else
                {
                    arr[counter++]=i;
                    arr[counter++]=n/i;
                }
            }
        }
    }
 
    public static int bs(int low,int high) 
    {
        while (low <high)
        {
            int mid = (low + high+1) / 2;
            if(brr[mid]>=l&&brr[mid]<=r)
            low=mid;
            else if(brr[mid]<l)
            {
                low=mid+1;
            }
            else if(brr[mid]>r)
            {
                high=mid-1;
            }
        }
        return low;
    }
    public static void main(String[] args)
    {
        PrintWriter out= new PrintWriter(System.out);
        Scanner sc = new Scanner(System.in);
        int a=sc.nextInt();
        int b=sc.nextInt();
        n=sc.nextLong();
        arr=new int[100000];
        counter=0;
        commDiv(a,b);
        brr=new int[counter];
        for(int i = 0 ;i<counter;i++)
        brr[i]=arr[i];
        Arrays.sort(brr);
        while(n-->0)
        {
            l=sc.nextInt();
            r=sc.nextInt();
            int index=bs(0,counter-1);
            if(index>=counter)
            System.out.println(-1);
            else if(!(brr[index]>=l&&brr[index]<=r))
            System.out.println(-1);
            else
            System.out.println(brr[index]);
        }
    }
}