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 static java.lang.Math.*;
import static java.lang.System.currentTimeMillis;
import static java.lang.System.exit;
import static java.lang.System.arraycopy;
import static java.util.Arrays.sort;
import static java.util.Arrays.binarySearch;
import static java.util.Arrays.fill;
import java.util.*;
import java.io.*;

public class Main {

	public static void main(String[] args) throws IOException {
		try {
			if (new File("input.txt").exists())
				System.setIn(new FileInputStream("input.txt"));
		} catch (SecurityException e) {
		}
		new Main().run();
	
	}

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st = new StringTokenizer("");
	
	int gcd(int a, int b){
		while(a > 0 && b > 0)
			if(a > b)
				a %= b;
			else
				b %= a;
		return a + b;
	}

	final int MAX = 1000000;
	int divs[] = new int[MAX];
	int V = 0;
	private void run() throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		
		int a = nextInt();
		int b = nextInt();
		int G = gcd(a, b);
		
		int B = G;
		divs[V++] = 1;
		
		for(int i = 2; i < MAX; i++){
			if(G % i == 0){
				divs[V++] = i;
				divs[V++] = G / i;
			}
			while(B % i == 0)
				B /= i;
		}
		
		if(B > 1)
			divs[V++] = B;
		divs[V++] = G;
		sort(divs, 0, V);
		
		int q = nextInt();
		for(int i = 0; i < q; i++){
			int x = nextInt();
			int y = nextInt();
			
			int left = 0;
			int right = V;
			while(right - left > 1){
				int mid = (left + right) / 2;
				if(divs[mid] > y)
					right = mid;
				else
					left = mid;
			}
			
			int v = (right + left) / 2;
			if(divs[v] >= x && divs[v] <= y)
				out.println(divs[v]);
			else
				if(divs[v + 1] >= x && divs[v + 1] <= y)
					out.println(divs[v + 1]);
				else
					if(v > 0 &&divs[v - 1] >= x && divs[v - 1] <= y)
						out.println(divs[v - 1]);
					else
						out.println(-1);
		}
		in.close();
		out.close();
	}

	void chk(boolean b) {
		if (b)
			return;
		System.out.println(new Error().getStackTrace()[1]);
		exit(999);
	}
	void deb(String fmt, Object... args) {
		System.out.printf(Locale.US, fmt + "%n", args);
	}
	String nextToken() throws IOException {
		while (!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}
	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}
	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}
	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
	String nextLine() throws IOException {
		st = new StringTokenizer("");
		return in.readLine();
	}
	boolean EOF() throws IOException {
		while (!st.hasMoreTokens()) {
			String s = in.readLine();
			if (s == null)
				return true;
			st = new StringTokenizer(s);
		}
		return false;
	}
}