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. 
/*
    This code is written by KESHAV DAGA
    @keshavkeshu
*/


import java.util.*;
import java.io.*;
public class Main  
{
    static FastReader in=new FastReader();
    static final Random random=new Random();
    static int mod=1000000007;
    static int inf=Integer.MAX_VALUE;
    static int ninf=Integer.MIN_VALUE;
    static HashMap<String,Integer>map=new HashMap<>();
    static String yes="YES",no="NO";

    public static void main(String args[]) throws IOException {
        /*
            This is main section or the coding part
            @keshavkeshu
        */
        int t=in.nextInt();
        StringBuilder res=new StringBuilder();
        while(t-->0)
        {
            // logic
            int n=in.nextInt(),m=in.nextInt();
            Set<Integer> set=new HashSet<>();
            int a=(n+m)/2;
            int b=n+m-a;
            for(int i=0;i<min(a,n)+1;i++)
            {
                if(n-i <= b)
                    set.add(n-i+a-i);
            }
            for(int i=0;i<min(b,n)+1;i++)
            {
                if(n-i <= a)
                    set.add(n-i+b-i);
            }
            int size=set.size();
            res.append(size+"\n");
            for(int x:set)
            {
                res.append(x+" ");
            }
            res.append("\n");
            
        }
        
        print(res);
    }
    
   
    //  2 1 
    // 1 2
   
   
    
    static int max(int a, int b)
    {
        if(a<b)
        	return b;
        return a;
    }
    
    static int min(int a, int b)
    {
        if(a>b)
        	return b;
        return a;
    }
    
    static long max(long a, long b)
    {
        if(a<b)
        	return b;
        return a;
    }
    
    static long min(long a, long b)
    {
        if(a>b)
        	return b;
        return a;
    }
    static int max(int a, int b, int c)
    {
        if(a>b && a>c)
        	return a;
        else if(b>a && b>c)
            return b;
        else
            return c;
    }
    
    static int min(int a, int b, int c)
    {
        if(a<b && a<c)
        	return a;
        else if(b<a && b<c)
            return b;
        else
            return c;
    }
    
     
    static void ruffleSort(int[] a) {
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static < E > void print(E res)
    {
        System.out.println(res);
    }
    
    static < E > void printd(E res)
    {
        System.out.println(res);
    }


    static  int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        return gcd(b,a%b);
    }
    
    static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }

    
    static int abs(int a)
    {
        if(a<0)
            return -1*a;
        return a;
    }

    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;
        }

        int [] ria(int n) {
            int res [] = new int [n];
            for(int i = 0; i<n; i++)res[i] = nextInt();
            return res;
        }
        long [] rla(int n) {
            long res [] = new long [n];
            for(int i = 0; i<n; i++)res[i] = nextLong();
            return res;
        }
    }

}
