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.io.*;
import java.math.*;
import java.util.*;

/**
 * @author Alexey Safronov (safronov.aa@gmail.com)
 */
public class C {
	private InputReader in;
	private PrintWriter out;
	
	public int gcd(int a, int b) {
		if(b == 0) {
			return a;
		}
		
		return gcd(b, a % b);
	}

	private void solve() {
		int a = in.readInt();
		int b = in.readInt();
		
		int max = gcd(a, b);
		
		ArrayList<Integer> a_div = new ArrayList<Integer>();
		HashSet<Integer> b_div = new HashSet<Integer>();
		
		
		int k = 1;
		while(k <= Math.sqrt(a)) {
			int c = a % k;
			int d = a / k;
			if(c == 0) {
				a_div.add(k);
				if(k != d) {
					a_div.add(d);
				}
			}
			++k;
		}
		
		k = 1;
		while(k <= Math.sqrt(b)) {
			int c = b % k;
			int d = b / k;
			if(c == 0) {
				b_div.add(k);
				if(k != d) {
					b_div.add(d);
				}
			}
			++k;
		}
		
		Collections.sort(a_div);
		int size = a_div.size();
		
		int n = in.readInt();
		
		for(int i = 0; i < n; i++) {
			int from = in.readInt();
			int to = in.readInt();
			
			if(from > max) {
				out.println(-1);
				continue;
			}
			
			int result = -1;
			
			for(int j = size - 1; j >= 0; j--) {
				int number = a_div.get(j);
				
				if(number >= from && number <= to) {
					if(b_div.contains(number)) {
						result = number;
						break;
					}
				}
			}
			
			out.println(result);
		}
	}

	public static void main(String[] args) {
		new C().run();
	}

	private C() {
		try {
//			System.setIn(new FileInputStream("input.txt"));
//			System.setOut(new PrintStream(new FileOutputStream("output.txt")));
		} catch (Exception e) {
			throw new RuntimeException(e);
		}
		in = new InputReader(System.in);
		out = new PrintWriter(System.out);
	}

	private void run() {
		//int tests = in.readInt();
		//for(int test = 1; test <= tests; ++test)
				solve();
			
		exit();
	}

	private void exit() {
		out.close();
		System.exit(0);
	}

	private static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar, numChars;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int readInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long readLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public String readString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuffer res = new StringBuffer();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private String readLine0() {
			StringBuffer buf = new StringBuffer();
			int c = read();
			while (c != '\n' && c != -1) {
				if (c != '\r')
					buf.appendCodePoint(c);
				c = read();
			}
			return buf.toString();
		}

		public String readLine() {
			String s = readLine0();
			while (s.trim().length() == 0)
				s = readLine0();
			return s;
		}

		public String readLine(boolean ignoreEmptyLines) {
			if (ignoreEmptyLines)
				return readLine();
			else
				return readLine0();
		}

		public BigInteger readBigInteger() {
			try {
				return new BigInteger(readString());
			} catch (NumberFormatException e) {
				throw new InputMismatchException();
			}
		}

		public char readCharacter() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			return (char) c;
		}

		public double readDouble() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') {
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, readInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') {
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) {
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, readInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
	}
}