Alice and Borys are playing tennis.

A tennis match consists of games. In each game, one of the players is serving and the other one is receiving.

Players serve in turns: after a game where Alice is serving follows a game where Borys is serving, and vice versa.

Each game ends with a victory of one of the players. If a game is won by the serving player, it's said that this player holds serve. If a game is won by the receiving player, it's said that this player breaks serve.

It is known that Alice won a games and Borys won b games during the match. It is unknown who served first and who won which games.

Find all values of k such that exactly k breaks could happen during the match between Alice and Borys in total.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^3). Description of the test cases follows.

Each of the next t lines describes one test case and contains two integers a and b (0 ≤ a, b ≤ 10^5; a + b > 0) — the number of games won by Alice and Borys, respectively.

It is guaranteed that the sum of a + b over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case print two lines.

In the first line, print a single integer m (1 ≤ m ≤ a + b + 1) — the number of values of k such that exactly k breaks could happen during the match.

In the second line, print m distinct integers k_1, k_2, …, k_m (0 ≤ k_1 < k_2 < … < k_m ≤ a + b) — the sought values of k in increasing order.

Example

Input


3
2 1
1 1
0 5


Output


4
0 1 2 3
2
0 2
2
2 3

Note

In the first test case, any number of breaks between 0 and 3 could happen during the match: 

  * Alice holds serve, Borys holds serve, Alice holds serve: 0 breaks; 
  * Borys holds serve, Alice holds serve, Alice breaks serve: 1 break; 
  * Borys breaks serve, Alice breaks serve, Alice holds serve: 2 breaks; 
  * Alice breaks serve, Borys breaks serve, Alice breaks serve: 3 breaks. 



In the second test case, the players could either both hold serves (0 breaks) or both break serves (2 breaks).

In the third test case, either 2 or 3 breaks could happen: 

  * Borys holds serve, Borys breaks serve, Borys holds serve, Borys breaks serve, Borys holds serve: 2 breaks; 
  * Borys breaks serve, Borys holds serve, Borys breaks serve, Borys holds serve, Borys breaks serve: 3 breaks. 

import java.io.*;
import java.util.*;
public class cp
{
	static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader()
		{
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException
		{
			din = new DataInputStream(
					new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException
		{
			byte[] buf = new byte[64]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n') {
					if (cnt != 0) {
						break;
					}
					else {
						continue;
					}
				}
				buf[cnt++] = (byte)c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException
		{
			int ret = 0;
			byte c = read();
			while (c <= ' ') {
				c = read();
			}
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException
		{
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException
		{
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException
		{
			bytesRead = din.read(buffer, bufferPointer = 0,
					BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException
		{
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException
		{
			if (din == null)
				return;
			din.close();
		}
	}

	public static boolean check(int arr[],int sort[]) {
		for(int i = 0;i < arr.length;i++) {
			if(arr[i] != sort[i]) {
				return true;
			}

		}
		return false;
	}

	public static Map<Integer, Integer>
	sortByKey(Map<Integer, Integer> hm)
	{
		// Create a list from elements of HashMap
		List<Map.Entry<Integer, Integer> > list
		= new LinkedList<Map.Entry<Integer, Integer> >(
				hm.entrySet());

		// Sort the list using lambda expression
		Collections.sort(
				list,
				(i1, i2) -> i1.getKey().compareTo(i2.getKey()));

		// put data from sorted list to hashmap
		HashMap<Integer, Integer> temp
		= new LinkedHashMap<Integer, Integer>();
		for (Map.Entry<Integer, Integer> aa : list) {
			temp.put(aa.getKey(), aa.getValue());
		}
		return temp;
	}


	public static void main(String[] args) throws IOException
	{
		try{
			//Your Solve
			Reader s = new Reader();
			//			Scanner s = new Scanner(System.in);
			int t = s.nextInt();

			for(int p = 0;p < t;p++) {
				int a = s.nextInt();
				int b = s.nextInt();
				int n = a+b;
				int e = (int)Math.ceil(n/2.0);
				int f = n/2;
				int y = 0;
				Map<Integer, Integer> mp = new HashMap<>();
				for(int x = 0;x <= e;x++ ) {
					y = a+x-e;
					if(y >= 0 && y <= f) {
						int breaks = x+y;
						if (mp.containsKey(breaks))
						{
							mp.put(breaks, mp.get(breaks) + 1);
						}
						else
						{
							mp.put(breaks, 1);
						}
					}
					
				}
				int g = (int)Math.ceil(n/2.0);
				int h = n/2;
				for(int x = 0;x <= h;x++ ) {
					y = a+x-h;
					if(y >= 0 && y <= g) {
						int breaks = x+y;
						if (mp.containsKey(breaks))
						{
							mp.put(breaks, mp.get(breaks) + 1);
						}
						else
						{
							mp.put(breaks, 1);
						}
					}
					
				}
				
				System.out.println(mp.size());
				   for (Map.Entry<Integer,Integer> entry : mp.entrySet()) {
			            System.out.print(entry.getKey() + " ");
				   }
				   System.out.println();
			}	



		}catch(Exception e){
			return;
		}
	}
}