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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    static int arr[];
    static int tree[];
    static int z =0;
    static int MAX = (int)1e7+1;
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner input = new Scanner(System.in);
		int a = input.nextInt();
		int b = input.nextInt();
		int q = input.nextInt();
		int gcd = euclids(a,b);
		arr = new int[MAX];
		Arrays.fill(arr,Integer.MAX_VALUE);
		z =0;
		for(int i =1;i*i<=gcd;i++){
		    if(gcd%i == 0){
		        arr[z++] = i;
		        if(gcd/i != i){
		            arr[z++] = gcd/i;
		        }
		    }
		}
		arr[z++] = gcd;
		Arrays.sort(arr);
		while(q-->0){
		    int l = input.nextInt();
		    int r = input.nextInt();
		    //int ql = binaryl(0,z-1,l);
		    int qr = binaryr(0,z-1,r);
		    if(arr[qr]<l){
		        System.out.println(-1);
		    }else{
		        System.out.println(arr[qr]);
		    }
		}
	}
	public static int euclids(int a,int b){
	    return b==0?a:euclids(b,a%b);
	}

	public static int binaryr(int l,int r,int val){
	    int ans = 0;
	    while(l<=r){
	        int mid = (l+r)/2;
	        if(arr[mid]<=val){
	            ans = mid;
	            l = mid+1;
	        }else{
	             r= mid-1;
	        }
	    }
	    return ans;
	}
}