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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Solver {

    public static void main(String[] args) {
        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        new TaskA().solveB(in, out);
        out.close();
    }

    static class TaskA {
        public void solveA(FastReader in, PrintWriter out) {
            int t = in.nextInt();

            while (t-- > 0) {
                int n = in.nextInt();
                int[] array = in.nextIntArray(n);
                int i = 0;

                while (true) {
                    if (isSorted(array)) {
                        break;
                    }
                    i++;

                    int j = i % 2 == 1 ? 0 : 1;
                    for (; j < array.length - 1; j += 2) {
                        if (array[j] > array[j+1]) {
                            int temp = array[j];
                            array[j] = array[j+1];
                            array[j+1] = temp;
                        }
                    }
                }

                out.println(i);
            }
        }

        private boolean isSorted(int[] array) {
            for (int i = 0; i < array.length - 1; i++) {
                if (array[i+1] < array[i]) {
                    return false;
                }
            }
            return true;
        }

        public void solveB(FastReader in, PrintWriter out) {
            int t = in.nextInt();

            while (t-- > 0) {
                int a = in.nextInt();
                int b = in.nextInt();

                int n = a + b;

                int min = Math.min(a, b);
                int minBreaks = (n - min * 2) / 2;
                int maxBreaks = (min * 2) + (int) Math.ceil((n - min) / 2.0);

                int interval = maxBreaks - minBreaks + 1;
                int even = n % 2 == 0 ? 2 : 1;

                out.println((interval / even));
                for (int i = minBreaks; i <= maxBreaks; i += even) {
                    out.print(i + " ");
                }
                out.println();
            }
        }

        public void solveC(FastReader in, PrintWriter out) {

        }

        public void solveD(FastReader in, PrintWriter out) {

        }

        public void solveE(FastReader in, PrintWriter out) {

        }
    }

    private static long gcd(long a, long b) {
        if (a == 0) {
            return b;
        }
        return gcd(b % a, a);
    }

    private static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    private static int min(int a, int b) {
        return a < b ? a : b;
    }

    private static int max(int a, int b) {
        return a > b ? a : b;
    }

    private static int min(ArrayList<Integer> list) {
        int min = Integer.MAX_VALUE;
        for (int el : list) {
            if (el < min) {
                min = el;
            }
        }
        return min;
    }

    private static int max(ArrayList<Integer> list) {
        int max = Integer.MIN_VALUE;
        for (int el : list) {
            if (el > max) {
                max = el;
            }
        }
        return max;
    }

    private static int min(int[] list) {
        int min = Integer.MAX_VALUE;
        for (int el : list) {
            if (el < min) {
                min = el;
            }
        }
        return min;
    }

    private static int max(int[] list) {
        int max = Integer.MIN_VALUE;
        for (int el : list) {
            if (el > max) {
                max = el;
            }
        }
        return max;
    }

    private static void fill(int[] array, int value) {
        for (int i = 0; i < array.length; i++) {
            array[i] = value;
        }
    }

    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[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextInt();
            }
            return array;
        }

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