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.*;
public class Ishani {
public static int findgcd(int a,int b){
if(b==0)return a;
return findgcd(b,a%b);	
}	
public static void main(String [] args){
Scanner in=new Scanner(System.in);
int a=in.nextInt();
int b=in.nextInt();
int n=in.nextInt();
int gcd=findgcd(Math.max(a,b),Math.min(a,b));
TreeSet<Integer>ts=new TreeSet<Integer>();
for(int i=1;i*i<=gcd;i++){
if(gcd%i==0){	
ts.add(i);
ts.add(gcd/i);		
}
}
StringBuilder sb=new StringBuilder();
//System.out.println(ts);
for(int i=0;i<n;i++){
int low=in.nextInt();
int high=in.nextInt();
int ans=-1;	
for(Integer x: ts){
 if(x>=low && x<=high)
 	ans=Math.max(ans,x);	
}
sb.append(ans);
sb.append('\n');	
}
System.out.println(sb);
}
}