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 codeForces.round740;

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.Set;
import java.util.StringTokenizer;

public class TestB {
	public static void main(String args[]) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine().trim());
		var sb = new StringBuilder();
		while(t-- > 0){
			int arr[] = nextIntArray(2, br);
			sb.append(solveQuery(arr)).append("\n");
		}
		br.close();
		System.out.println(sb);
	}

	private static String solveQuery(int arr[]){
		var sb = new StringBuilder();
		Set<Integer> hSet = new HashSet<>();
		swap(arr);

		int total = arr[0] + arr[1];
		int first = (int)Math.floor(((double)total) / 2);
		int second = total - first;
		

		// A Goes First
		for(int i = 0; i <= Math.min(arr[1], first); i++){
			int otherBreaks = arr[0] - (first - i);
			hSet.add(i+otherBreaks);
		}

		// A Decides Breaks
		for(int i = 0; i <= Math.min(arr[1], second); i++){
			int otherBreaks = arr[0] - (second - i);
			hSet.add(i + otherBreaks);
		}

		sb.append(hSet.size()).append("\n");
		for(int i: hSet) sb.append(i).append(" ");
		return sb.toString();
	}

	private static void swap(int arr[]){
		if(arr[0] < arr[1]){
			int temp = arr[0];
			arr[0] = arr[1];
			arr[1] = temp;
		}
	}

	private static int[] nextIntArray(int N, BufferedReader br) throws Exception {
		StringTokenizer st = new StringTokenizer(br.readLine().trim()," ");
		int arr[] = new int[N];
		for(int i = 0; i < N; i++)
			arr[i] = Integer.parseInt(st.nextToken());
		return arr;
	}
}
