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.*;
import java.util.*;
 
public class _1561b {
    FastScanner scn;
    PrintWriter w;
    PrintStream fs;

    long MOD = 1000000007;
    int N=100000+10;
    long mul(long x, long y) {long res = x * y; return (res >= MOD ? res % MOD : res);}
    long power(long x, long y) {if (y < 0) return 1; long res = 1; x %= MOD; while (y!=0) {if ((y & 1)==1)res = mul(res, x); y >>= 1; x = mul(x, x);} return res;}
    void ruffleSort(int[] a) {int n=a.length;Random r=new Random();for (int i=0; i<a.length; i++) {int oi=r.nextInt(n), temp=a[i];a[i]=a[oi];a[oi]=temp;}Arrays.sort(a);}
    boolean LOCAL;
    void debug(Object... o){if(LOCAL)System.err.println(Arrays.deepToString(o));}
    
    void solve(){

        int t=scn.nextInt();
            while(t-->0)
            {
                int a=scn.nextInt(),b=scn.nextInt();
                int s=a+b;
                if((s&1)==0){
                int min=Integer.MAX_VALUE,max=Integer.MIN_VALUE;
                    int turns=s/2;
                    if(a==turns&&b==turns){
                        min=0;
                        max=s;
                    }else{
                        if(a>s/2){
                            min=a-s/2;
                        }else if(b>s/2){
                            min=b-s/2;
                        }
                        max=(s/2)+(s/2-min);
                    }
                    HashSet<Integer> hs=new HashSet<>();
                    for(int i=min;i<=max;i+=2){
                        hs.add(i);
                    }
                    w.println(hs.size());
                    for(int e:hs){
                        w.print(e+" ");
                    }
                    w.println();
                }else{
                int min=Integer.MAX_VALUE,max=Integer.MIN_VALUE;
                int minTurns=s/2;
                int maxTurns=minTurns+1;
                    if(a>=maxTurns){
                        min=a-maxTurns;
                    }else if(b>=maxTurns){
                        min=b-maxTurns;
                    }
                    max=maxTurns+(minTurns-min);
                    HashSet<Integer> hs=new HashSet<>();
                    for(int i=min;i<=max;i++){
                        hs.add(i);
                    }
                    w.println(hs.size());
                    for(int e:hs){
                        w.print(e+" ");
                    }
                    w.println();
                }
            
            
            }
        
    }
 
    void run() {
        try {
            long ct = System.currentTimeMillis();
            scn = new FastScanner(new File("input.txt"));
            w = new PrintWriter(new File("output.txt"));
            fs=new PrintStream("error.txt");
            System.setErr(fs);
            LOCAL=true;
 
            solve();
 
            w.close();
            System.err.println(System.currentTimeMillis() - ct);
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }
 
    void runIO() {
 
        scn = new FastScanner(System.in);
        w = new PrintWriter(System.out);
        LOCAL=false;
 
        solve();
 
        w.close();
    }
 
    class FastScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }
 
        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }
 
        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }
 
        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
        
        int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        long[] nextLongArray(int n) {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
 
    public static void main(String[] args) {
        new _1561b().runIO();
    }
}
