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.*;
public class B {
    // static long mod = (long)Math.pow(10,9)+7;
	static Scanner sc = null;
// 	static int n;
// 	static Map<Integer,ArrayList<Integer>> map;
// 	static boolean visited[];
// 	static long val[];
// 	static long dis[];
// 	static long dp[][];
// 	static int N = 2*(int)Math.pow(10,5)+5;
// 	static int max = Integer.MAX_VALUE;
// 	static int K = 1001;
public static void main(String[] args){
	//System.out.println("Enter :");
	sc = new Scanner(System.in);
     int t = sc.nextInt();
     while(t-->0){
         int a = sc.nextInt();
         int b = sc.nextInt();
         int sum = a+b;
         ArrayList<Integer> ar = new ArrayList<>();
         if(sum%2==0){
        	 int n1 = sum/2;
             for(int i=0;i<=n1;i++) {
            	 int won = a-i;
            	 if(won<0)
            		 continue;
            	 int brea = n1-i+won;
            	 ar.add(brea);
             }
         }
         else{
             int n1 = sum/2;
             int n2 = sum/2+1;
             for(int i=0;i<=n1;i++) {
            	 int won = a-i;
            	 if(won<0 || won>n2)
            		 continue;
            	 int brea = n1-i+won;
            	 ar.add(brea);
             }
             for(int i=0;i<=n2;i++) {
            	 int won = a-i;
            	 if(won<0 || won>n1)
            		 continue;
            	 int brea = n2-i+won;
            	 ar.add( brea); 
             }
         }
         Collections.sort(ar);
         System.out.println(ar.size());
         for(Integer j : ar)
         System.out.print(j+" ");
         System.out.println();
     }
  }
}