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 first;//提交代码时，此行要注释掉
import java.math.BigDecimal;//小数
import java.math.BigInteger;//整数
import java.util.*;
public class Main{
	static int N =10100;
	public static void main(String args[]) {
		Scanner cin = new Scanner(System.in);
		int a,b,n,x,y,s[] =new int[N],m,k=0,mid,l,r,ans;
		a = cin.nextInt();
		b = cin.nextInt();
		m = gcd(a,b);
		for(int i = 1;i*i<=m;i++) {
			if(m%i==0) {
				s[++k] = i;
			if(i*i!=m)
				s[++k] =m/i;
			}
		}
		Arrays.sort(s,1,k+1);
		n = cin.nextInt();
		while(n!=0) {
			x = cin.nextInt();
			y = cin.nextInt();
			l = 1;r = k;ans =-1;
			while(l<=r) {
				mid =(l+r)/2;
				if(s[mid] > y)
				r = mid -1;
				else {
					l =mid +1;
					if(s[mid] >=x)
						ans =s[mid];
				}
			}
			System.out.println(ans);
			n--;
		}
	}
	public static int gcd(int a,int b) {
		if(b==0)
			return a;
		else
			return gcd(b,a%b);
	}
}