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.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class B_Charmed_by_the_Game {

      static Scanner in=new Scanner();
    
    static PrintWriter out=new PrintWriter( new OutputStreamWriter(System.out) );
    
    static int m;
    
    static long k[];
    
    static void solve(){
        
        out.println( (k[0]+k[1]+1) );
        out.flush();
        
        for(int i=0;i<k[0]+k[1]+1;i++ ){
            
            out.print(i+" ");
            out.flush();
            
        }
        
        out.println();
        out.flush();
        
    }
    
    public static void main(String[] amit) throws IOException {
        
        m=in.nextInt();
        
        for(int t=0;t<m;t++){
            
            k=new long[2];
            
            for(int i=0;i<2;i++){
            
                k[i]=in.nextLong();
                
            }
            
            solve();
            
        }
        
    }
 
     static class Scanner{
        
        BufferedReader in;
        StringTokenizer st;

        public Scanner() {
        
            in=new BufferedReader( new InputStreamReader(System.in) );
            
        }
        
        String next() throws IOException{
            
            while(st==null || !st.hasMoreElements()){
                
                st=new StringTokenizer(in.readLine());
                
            }
            
            return st.nextToken();
            
        }
        
        int nextInt() throws IOException{
            
            return Integer.parseInt(next());
            
        }
        
        long nextLong() throws IOException{
            
            return Long.parseLong(next());
            
        }
        
        String nextLine() throws IOException{
            
            return in.readLine();
            
        }
        
        char nextChar() throws IOException{
            
            return next().charAt(0);
            
        }
        
        double nextDouble() throws IOException{
            
            return Double.parseDouble(next());
            
        }
        
        float nextFloat() throws IOException{
            
            return Float.parseFloat(next());
            
        }
        
        boolean nextBoolean() throws IOException{
            
            return Boolean.parseBoolean(next());
            
        }
        
        void close() throws IOException{
            
            in.close();
            
        }
        
    }
    
}
