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. 
/*
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                      o8888888o
                      88" . "88
                      (| -_- |)
                      0\  =  /0
                    ___/`---'\___
                  .' \\|     |// '.
                 / \\|||  :  |||// \
                / _||||| -:- |||||- \
               |   | \\\  -  /// |   |
               | \_|  ''\---/''  |_/ |
               \  .-\__  '-'  ___/-. /
             ___'. .'  /--.--\  `. .'___
          ."" '<  `.___\_<|>_/___.' >' "".
         | | :  `- \`.;`\ _ /`;.`/ - ` : | |
         \  \ `_.   \_ __\ /__ _/   .-` /  /
     =====`-.____`.___ \_____/___.-`___.-'=====
                       `=---='
 
*/
import java.util.function.Consumer;
import java.util.*;
import java.math.*;
import java.io.*;
import java.lang.Math.*;

public class KickStart2020 {
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

		long nextLong() {
			return Long.parseLong(next());
		}

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

		float nextFloat() {
			return Float.parseFloat(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	static long gcd(long a, long b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);

	}

	public static class Pair implements Comparable<Pair> {
		public int index;
		public int value;

		public Pair(int index, int value) {
			this.index = index;
			this.value = value;
		}

		@Override
		public int compareTo(Pair other) {
			// multiplied to -1 as the author need descending sort order
			return -1 * Integer.valueOf(this.value).compareTo(other.value);
		}
	}

	static boolean isPrime(long d) {
		if (d == 1)
			return true;
		for (int i = 2; i <= (long) Math.sqrt(d); i++) {
			if (d % i == 0)
				return false;
		}
		return true;
	}

	static void decimalTob(long n, int b, int arr[], int i) {
		long z = n % b;
		arr[i] += (int)z;
		n /= b;
		if (n > 0) {
			i++;
			 decimalTob(n, b,arr, i);
		}
	}

	static long powermod(long x, long y, long mod) {
		long ans = 1;
		x = x % mod;
		if (x == 0)
			return 0;
		int i = 1;
		while (y > 0) {
			if ((y & 1) != 0)
				ans = (ans * x) % mod;
			y = y >> 1;
			x = (x * x) % mod;
		}
		return ans;
	}
	static boolean isSorted(int arr[]) {
		for(int i = 1; i <= arr.length; i++) if(arr[i -1] != i) return false;
		return true;
	}
	public static void main(String[] args) throws Exception {
		FastReader sc = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int t = sc.nextInt();
		outerloop:
			while(t-- > 0) {
               int n = sc.nextInt();
               int m = sc.nextInt();
               int diff = Math.abs(m - n);
               int z = Math.min(n, m);
               TreeSet<Integer> ss = new TreeSet<Integer>();
               int a = diff / 2;
               int b = (diff + 1) / 2;
               for(int i = 0; i <= z; i++) {
            	   ss.add(a + i * 2);
            	   ss.add(b + i * 2);
               }
               out.println(ss.size());
               for(int e: ss) out.print(e + " ");
               out.println();
			}
           out.close();
	 }
}