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.util.*;

import java.io.*;
import java.net.StandardSocketOptions;

public class tr0 {
	static PrintWriter out;
	static StringBuilder sb;
	static long mod = (long) 1e9 + 7;
	static long inf = (long) 1e16;
	static int n, k;
	static ArrayList<Integer>[] ad;
	static int[][] remove, add;
	static int[][] memo;
	static boolean vis[];
	static long[] inv, ncr[];
	static HashMap<Integer, Integer> hm;
	static int[] pre, suf, Smax[], Smin[];
	static int idmax, idmin;
	static ArrayList<Integer> av;
	static HashMap<Integer, Integer> mm;
	static boolean[] msks;
	static int[] lazy[], lazyCount;
	static int[] dist;
	static int[][] P;
	static long N;
	static ArrayList<Integer> gl;
	static int[] a;
	static String s;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		int t = sc.nextInt();
		while (t-- > 0) {
			Queue<Integer> q = new LinkedList<Integer>();
			int a = sc.nextInt();
			int b = sc.nextInt();
			int turns = a + b;
			for (int k = 0; k <= turns; k++) {
				int at = (turns + 1) / 2;
				int bt = turns / 2;
				boolean f = false;
				if (k == 2) {
		//			System.out.println(at + " " + bt);
				}
				if (at == a) {
					if (k % 2 == 0 && (at + 1) / 2 >= k/2 && (bt + 1) / 2 >= k/2)
						f = true;
				} else if (at < a) {
					int k1 = k;
					k1 -= a - at;
					bt += a - at;
					if (k1 >= 0) {
						if (k1 % 2 == 0 && (a + 1) / 2 >= k1/2 && (b + 1) / 2 >= k1/2)
							f = true;
					}
				} else {
					int k1 = k;
					k1 -= b - bt;
					bt += b - bt;
					if (k1 >= 0) {
						if (k1 % 2 == 0 && (a + 1) / 2 >= k1/2 && (b + 1) / 2 >= k1/2)
							f = true;
					}
				}
				at = turns / 2;
				bt = (turns + 1) / 2;

				if (at == a) {
					if (k % 2 == 0 && (at + 1) / 2 >= k/2 && (bt + 1) / 2 >= k/2)
						f = true;
				} else if (at < a) {
					int k1 = k;
					k1 -= a - at;
					bt += a - at;
					if (k1 >= 0) {
						if (k1 % 2 == 0 && (a + 1) / 2 >= k1/2 && (b + 1) / 2 >= k1/2)
							f = true;
					}
				} else {
					int k1 = k;
					k1 -= b - bt;
					bt += b - bt;
					if (k1 >= 0) {
						if (k1 % 2 == 0 && (a + 1) / 2 >= k1/2 && (b + 1) / 2 >= k1/2)
							f = true;
					}
				}
				if (f)
					q.add(k);
			}
			out.println(q.size());
			for (int h : q)
				out.print(h + " ");
			out.println();
		}
		out.flush();
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public int[] nextArrInt(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextArrLong(int n) throws IOException {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public int[] nextArrIntSorted(int n) throws IOException {
			int[] a = new int[n];
			Integer[] a1 = new Integer[n];
			for (int i = 0; i < n; i++)
				a1[i] = nextInt();
			Arrays.sort(a1);
			for (int i = 0; i < n; i++)
				a[i] = a1[i].intValue();
			return a;
		}

		public long[] nextArrLongSorted(int n) throws IOException {
			long[] a = new long[n];
			Long[] a1 = new Long[n];
			for (int i = 0; i < n; i++)
				a1[i] = nextLong();
			Arrays.sort(a1);
			for (int i = 0; i < n; i++)
				a[i] = a1[i].longValue();
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}