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 B {
	
	public static void main(String[] args)throws IOException {
		
		FastScanner scan = new FastScanner();
		BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));
		int t = scan.nextInt();
		for(int tt = 0;tt<t;tt++) {
			
			int a = scan.nextInt();
			int b = scan.nextInt();
			int tot = a+b;
			int diff = Math.abs(a-b)/2;
			ArrayList<Integer> list = new ArrayList<>();
			for(int i = diff; i<=a+b-diff;i++) {
				if(tot%2==0) {
					if(i%2==0) list.add(i);
				}
				else {
					list.add(i);
				}
			}
			output.write(list.size() + "\n");
			for(Integer i: list) output.write(i+" ");
			output.write("\n");
		}
		output.flush();

	}
	
	public static int[] sort(int arr[]) {

		List<Integer> list = new ArrayList<>();
		for(int i:arr)
			list.add(i);
		Collections.sort(list);
		for(int i = 0;i<list.size();i++) {
			arr[i] = list.get(i);
		}
		return arr;

	}
	
	public static int gcd(int a, int b) {
		if(a == 0) return b;
		return gcd(b%a, a);
	}
	
	public static void printArray(int arr[]) {
		for(int i:arr) System.out.print(i+" ");
		System.out.println();
	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
		
		double nextDouble() {
			return Double.parseDouble(next());
		}
	}

}
