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 MyPackage;
import java.io.*;
import java.util.*;
public class MyClass {
    final static long mod = 1_000_000_007;
    final static int mini = Integer.MIN_VALUE;
    final static int maxi = Integer.MAX_VALUE;
    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
    static long ncr(long n, long r) {
        if (r > n - r) r = n - r;
        long[] C = new long[(int) r + 1];
        C[0] = 1;
        for (int i = 1; i <= n; i++) {
            for (long j = Math.min(i, r); j > 0; j--)
                C[(int) j] = (C[(int) j] + C[(int) j - 1]) % mod;
        }
        return C[(int) r];
    }
    static boolean isPrime(long n) {
        if (n <= 1)
            return false;
        else if (n == 2)
            return true;
        else if (n % 2 == 0)
            return false;
        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            if (n % i == 0)
                return false;
        }
        return true;
    }
    static boolean isSquare(long x) {
        if (x >= 0) {
            long sr = (long) Math.sqrt(x);
            return ((sr * sr) == x);
        }
        return false;
    }
    static int countSetBits(int n) {
        int count = 0;
        while(n > 0) {
            n &= (n - 1);
            count++;
        }
        return count;
    }
    static int digits(long n) {
        int count = 0;
        long temp = n;
        while (temp > 0) {
            temp /= 10;
            count++;
        }
        return count;
    }
    static boolean isPalindrome(long i) {
        long originalNum = i;
        long remainder;
        long reversedNum = 0;
        while (i != 0) {
            remainder = i % 10;
            reversedNum = reversedNum * 10 + remainder;
            i /= 10;
        }
        return originalNum == reversedNum;
    }
    static long lcm(long a, long b) {
        return (a / gcd(a, b)) * b;
    }
    static void sort(long[] a) {
        ArrayList<Long> l = new ArrayList<>();
        for (long value : a) {
            l.add(value);
        }
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a[i] = l.get(i);
    }
    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int value : a) {
            l.add(value);
        }
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a[i] = l.get(i);
    }
    static void reverse(int[] arr) {
        int l = 0;
        int h = arr.length - 1;
        while (l < h) {
            swap(arr, l, h);
            l++;
            h--;
        }
    }
    static String reverse(String s) {
        StringBuilder res = new StringBuilder(s);
        return res.reverse().toString();
    }
    static long fact(long n) {
        long res = 1, i;
        for (i = 2; i <= n; i++)
            res *= i;
        return res;
    }
    static void swap(int[] arr, int i, int j) {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String n() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nint() {
            return Integer.parseInt(n());
        }

        long nlong() {
            return Long.parseLong(n());
        }

        double ndouble() {
            return Double.parseDouble(n());
        }

        int[] narr(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nint();
            return a;
        }

        int[][] narr(int n, int m) {
            int[][] a = new int[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    a[i][j] = nint();
            return a;
        }

        String nline() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    public static class Pair {
        long a;
        long b;

        public Pair(long a, long b) {
            this.a = a;
            this.b = b;
        }
    }
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        int t = sc.nint();
        while(t-- > 0) {
            int a = sc.nint();
            int b = sc.nint();
            Set<Integer> set = new HashSet<>();
            int tot = a + b;
            int f = tot / 2;
            int s = tot - f;
            for(int i = 0; i <= Math.min(a, f); i++) {
                if(a - i <= s) {
                    set.add(a - i + f - i);
                }
            }
            for(int i = 0; i <= Math.min(a, s); i++) {
                if(a - i <= f) {
                    set.add(a - i + s - i);
                }
            }
            out.println(set.size());
            for(int i : set) {
                out.print(i + " ");
            }
            out.println();
        }
        out.flush();
        out.close();
    }
}