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.InputStreamReader;
import java.util.StringTokenizer;
import java.util.*;
import java.io.*;
public class Main {
    public static void main(String args[])throws Exception{
        Input sc=new Input();
        StringBuilder sb=new StringBuilder();
        int t=sc.readInt();
        for(int f=0;f<t;f++){
            int d[]=sc.readArray();
            int a=d[0];
            int b=d[1];
            int arr[]=new int[a+b+1];// 1 2 1 2 1
                                     // 2 1 2 1 1
                                     // 1 2 1 1 2
                                     // 2 1 1 2 1

            int n=a+b;
            int temp=Math.max(a,b);
            a= (Math.min(a, b));
            b=temp;
            for(int i=0;i<=n/2;i++){
                int x=n/2;
                int y= n-x;
                if((x-i==a && y+i==b) || (x+i==b && y-i==a)){
                    arr[i]++;
                    arr[n-i]++;
                }
//                if(a>=i && a!=0){
//                    arr[i]++;
//                    arr[n-i]++;
//                }

            }
//            for(int i=0;i<a+b+1;i++){
//                System.out.print(arr[i]+" ");
//            }
//            System.out.println();
            int count=0;
            for(int i=0;i<=n;i++){
                if(arr[i]!=0)
                    count++;
            }
            sb.append(count+"\n");
            for(int i=0;i<=n;i++)
            {
                if(arr[i]!=0)
                    sb.append(i+" ");
            }
            sb.append("\n");
        }
        System.out.print(sb);
    }
}
class Input{
    BufferedReader br;
    StringTokenizer st;
    Input(){
        br=new BufferedReader(new InputStreamReader(System.in));
        st=new StringTokenizer("");
    }
    public int[] readArray() throws Exception{
        st=new StringTokenizer(br.readLine());
        int a[]=new int[st.countTokens()];
        for(int i=0;i<a.length;i++){
            a[i]=Integer.parseInt(st.nextToken());
        }
        return a;
    }
    public long[] readArrayLong() throws Exception{
        st=new StringTokenizer(br.readLine());
        long a[]=new long[st.countTokens()];
        for(int i=0;i<a.length;i++){
            a[i]=Long.parseLong(st.nextToken());
        }
        return a;
    }
    public int readInt() throws Exception{
        st=new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }
    public long readLong() throws Exception{
        st=new StringTokenizer(br.readLine());
        return Long.parseLong(st.nextToken());
    }
    public String readString() throws Exception{
        return br.readLine();
    }
    public int[][] read2dArray(int n,int m)throws Exception{
        int a[][]=new int[n][m];
        for(int i=0;i<n;i++){
            st=new StringTokenizer(br.readLine());
            for(int j=0;j<m;j++){
                a[i][j]=Integer.parseInt(st.nextToken());
            }
        }
        return a;
    }
}


