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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Practice {

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        StringBuilder sb = new StringBuilder();
        while (t-->0){
            int alice = sc.nextInt(); int bob = sc.nextInt();
            HashSet<Integer> ans = new HashSet<>();
            int serve1 = (alice+bob+1)/2;
            findBreaks(serve1, alice, bob, ans);
            sb.append(ans.size());
            sb.append("\n");
            for(int x : ans){
                sb.append(x);
                sb.append(" ");
            }
            sb.append("\n");
        }
        System.out.println(sb.toString().trim());
    }

    private static void findBreaks(int serve,  int alice, int bob, HashSet<Integer> ans) {
        for(int i=0;i<=serve;i++){
            for(int j=0;j<=serve;j++){
                if(isValid(i, j, alice, bob)){
                    ans.add(i+j);
                }
            }
        }
    }

    private static boolean isValid(int aliceBreak, int bobBreaks, int alice, int bob) {
        if(aliceBreak>alice || bobBreaks > bob) return false;
        int serve1 = (alice+bob+1)/2; int serve2 = alice+bob-serve1;
        return isValidAll(serve1, serve2, aliceBreak, bobBreaks, alice, bob) || isValidAll(serve2, serve1, aliceBreak, bobBreaks, alice, bob);
    }

    private static boolean isValidAll(int aliceServe, int bobServe, int aliceBreak, int bobBreaks, int aliceWin, int bobWin) {
        int aliceServeWinning = aliceServe - bobBreaks;
        int bobServeWinning = bobServe -aliceBreak;

        if(aliceBreak+aliceServeWinning != aliceWin || bobServeWinning +  bobBreaks != bobWin) return false;
        return true;
    }
}