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:
//75C

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.StringTokenizer;

public class ModifiedGCD {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		
		StringTokenizer st = new StringTokenizer(br.readLine());
		
		int a = Integer.parseInt(st.nextToken());
		int b = Integer.parseInt(st.nextToken());
		
		int g = gcd (a,b);
		
		List<Integer> dividers = new ArrayList<Integer>();
		
		for (int i = 1; i < (int)Math.sqrt(g)+1; i++) {
			if (g%i == 0) {
				dividers.add(i);
				dividers.add(g/i);
			}
		}
		Collections.sort(dividers);
		
		int n = Integer.parseInt(br.readLine());
		
		for (int i = 0; i < n; i++) {
			st = new StringTokenizer(br.readLine());
			
			int l = Integer.parseInt(st.nextToken());
			int h = Integer.parseInt(st.nextToken());
			
			int bs = Collections.binarySearch(dividers, h);
			
			if (bs >= 0) {
				System.out.println(h);
			}
			else if (bs == -1 || dividers.get(-bs-2) < l) {
				System.out.println(-1);
			}
			else {
				System.out.println(dividers.get(-bs-2));
			}
		}
	}

	private static int gcd(int a, int b) {
		return a < b ? euc(b, a) : euc(a, b);
	}

	private static int euc(int a, int b) {
		return b == 0 ? a : euc(b, a%b);
	}
}