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.text.DecimalFormat;
import java.util.Scanner;
import java.util.*;
public class Test1 {


    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
//            测试次数
        int testnum = s.nextInt();


        for (int k = 0; k <testnum; k++) {
//
            int a=s.nextInt();
            int b=s.nextInt();

            int A=Math.max(a,b);
            int B=Math.min(a,b);
            Set<Integer> ans = new HashSet<>();

            int sum=A+B;
            if(A-B<=1){
            for (int i = 0; i <=sum; i++) {
                if(i%2==0){
                    ans.add(i);
                    ans.add(sum-i);
                }
            }
                System.out.println(ans.size());

            for(int i:ans){

                System.out.print(i);
                System.out.print(" ");
            }
                System.out.println();
            }else{
                for (int i = A-(sum+1)/2; i < (sum+1)/2; i+=3) {

                        ans.add(i);
                        ans.add(sum-i);

                }
                System.out.println(ans.size());

                for(int i:ans){

                    System.out.print(i);
                    System.out.print(" ");
                }
                System.out.println();

            }




        }


    }





    private static boolean check(int breaks,int a,int b) {
        int sum=a+b;
        int A=(sum+1)/2;
        int B=sum-A;
        if(breaks==a-A){
            return true;
        }
        return false;

    }
}
