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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.*;

public class Solution {
	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());
        }
 
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }		
	
	static class Pair {
	    int x;
	    int y;
	  
	    // Constructor
	public Pair(int x, int y)
	    {
	        this.x = x;
	        this.y = y;
	    }
	}
	
	public static void swap(int i, int[] arr) {
		int temp = arr[i];
		arr[i] = arr[i+1];
		arr[i+1] = temp;
	
}

	public static boolean sorted(int arr[]) {
		for(int i=0; i<arr.length; i++) {
			if(arr[i]!=i+1) return false;
		}
		return true;
	}
	public static void main(String[] args) throws IOException{
		
		FastReader sc = new FastReader();
		BufferedWriter output=new BufferedWriter(new OutputStreamWriter(System.out));
		int t= sc.nextInt();
		while(t--!=0) {
        int n = sc.nextInt();
        int m = sc.nextInt();
        int l = (n+m)/2 - Math.min(n, m);
        int r = (n+m+1)/2 + Math.min(n, m);
        if((n+m)%2==0) {
        	output.write((r-l)/2+"\n");
        	for(int i=l;i<=r;i+=2) {
        		output.write(i+" ");
        	}
        	output.write("\n");
        }
        else{
        	output.write((r-l)+"\n");
        	for(int i=l;i<=r;i++) {
        		output.write(i+" ");
        	}
        	output.write("\n");
        }
		
		
//		for(int i=0; i<n; i++) {
//			arr[i] = sc.nextInt();
//		}
		
		
		//int ans=0;	

		
		//output.write(l+" "+r+"\n");
		}
		output.flush();
	}
	
					
}
