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. 
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main(String[] args) {
		FastReader s = new FastReader();
		PrintWriter out  = new PrintWriter(System.out);
		//out.println();
		int tc = s.nextInt();
		while (tc-- > 0) {
		    int a = s.nextInt();
		    int b = s.nextInt();
		    int d =  Math.abs(a-b)/2;
		    ArrayList<Integer> al = new ArrayList<Integer>();
		    if(((a+b)&1) == 0){
		        for(int i = d ; i <= a+b-d ; i+=2){
		            al.add(i);
		        }
		    }
		    else{
		        for(int i = 0 ; i <= a+b-d ; i++){
		            al.add(i);
		        }
		    }
		    out.println(al.size());
		    for(int i : al){
		        out.print(i+" ");
		    }
		    out.println();
		}
		out.flush();
	}
	
	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 int MOD = 1000000007;
	
	public static long power(long x,int y){
	    long res = 1;
	    
	    x = x%MOD;
	    
	    while(y > 0){
	        if((y&1) > 0)
	            res = (res*x) % MOD;
	            
	        y = y >> 1;
	        x = (x*x) % MOD;
	    }
	    
	    return res;
	}
	
	public static ArrayList<Integer> seive(int n){
	    boolean[] isPrime = new boolean[n+1];
	    
	    Arrays.fill(isPrime,true);
	    
	    isPrime[0] = isPrime[1] = false;
	    
	    for(int i = 2 ; i * i <= n ; i++){
	        if(isPrime[i]){
	            for(int j = i*i ; j <= n ; j += i){
	                isPrime[j] = false;
	            }
	        }
	    }
	    
	    ArrayList<Integer> prime = new ArrayList<>();
	    
	    for(int i  = 0 ; i <= n ; i++){
	        if(isPrime[i]){
	            prime.add(i);        
	        }
	    }
	    
	    return prime;
	}
}
