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. 
/**
 * @author -- Sourav Joshi
 */

//			               _,--"^^"-.,_
//			         _.-"~^`~-.    .-~`^~"-._
//			     ,="`"-._     .----.     _.-"`"=,
//			    ;_       "-. (0 )( 0) .-"       _;
//			   .' `~"=,_    '.\ \/ /.'    _,="~` `.
//			   ;_       "-. _.-)  (-._ .-"       _;
//			   : ^~"-.,___.'  (    )  `.___,.-"~^ ;
//			   :        _:     `--'     :_        :
//			    '._,-~"` :':          :': `"~-,_.'
//			       '.,_.-`.            .'`-._,.'
//			          :__.-`-.______.-'`-.__;
//			                 //    \\
//			               (((~    ~)))

import java.util.*;


import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import static java.lang.Math.ceil;
import static java.lang.Math.max;
import static java.lang.Math.pow;
import java.io.*;

public class Solution {

	static FastScanner s = new FastScanner();
	static FastWriter out = new FastWriter();
	final static long mod = 1000000000 + 7;
	final static int INT_MAX = Integer.MAX_VALUE;
	final static int INT_MIN = Integer.MIN_VALUE;
	final static long LONG_MAX = Long.MAX_VALUE;
	final static long LONG_MIN = Long.MIN_VALUE;
	final static double DOUBLE_MAX = Double.MAX_VALUE;
	final static double DOUBLE_MIN = Double.MIN_VALUE;
	final static float FLOAT_MAX = Float.MAX_VALUE;
	final static float FLOAT_MIN = Float.MIN_VALUE;


	static class Pair<T,R>{
		T first;
		R Second;
	}

	static class FastScanner{
		BufferedReader br;
		StringTokenizer st;

		public FastScanner() {
			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;
		}
	}

	static class FastWriter{
		private final BufferedWriter bw;

		public FastWriter() {
			this.bw = new BufferedWriter(new OutputStreamWriter(System.out));
		}

		public void print(Object object) throws IOException{
			bw.append(""+ object);
		}

		public void println(Object object) throws IOException{
			print(object);
			bw.append("\n");
		}

		public void close() throws IOException{
			bw.close();
		}
	}

	public static void f(int arr[], int n, int b, int i, Set<Integer> ans) {
		if(i == arr.length) {
			if(n == 0) {
				ans.add(b);
				return;
			}else {
				return;
			}
		}
		
		if(i%2 == 0) {
			arr[i] = 1;
			f(arr, n-1, b, i+1, ans);
			arr[i] = 0;
			f(arr, n, b+1, i+1, ans);
			arr[i] = 0;
		}else {
			arr[i] = 1;
			f(arr, n-1, b+1, i+1, ans);
			arr[i] = 0;
			f(arr, n, b, i+1, ans);
			arr[i] = 0;
		}
		
	}
	
	
	
	public static void s(int arr[], int n, int b, int i, Set<Integer> ans) {
		if(i == arr.length) {
			if(n == 0) {
				ans.add(b);
				return;
			}else {
				return;
			}
		}
		
		if(i%2 == 1) {
			arr[i] = 1;
			s(arr, n-1, b, i+1, ans);
			arr[i] = 0;
			s(arr, n, b+1, i+1, ans);
			arr[i] = 0;
		}else {
			arr[i] = 1;
			s(arr, n-1, b+1, i+1, ans);
			arr[i] = 0;
			s(arr, n, b, i+1, ans);
			arr[i] = 0;
		}
		
	}

	

	public static void main(String[] args) throws IOException {
		int test = s.nextInt();
		while(test-->0) {
			int a = s.nextInt();
			int b = s.nextInt();
			int total = a+b;
			int op1 = total/2;
			int op2 = total-op1;
			Set<Integer> ans = new HashSet<Integer>();
			for(int i = 0; i <= op1; i++) {
				if((op2 + i >= a) && i <= a) {
					int br = (op1 - i) + (a - i);
					ans.add(br);
				}
			}
			for(int i = 0; i <= op2; i++) {
				if((op1 + i >= a) && i <= a) {
					int br = (op2 - i) + (a - i);
					ans.add(br);
				}
			}
			out.println(ans.size());
			for(int i : ans) {
				out.print(i+" ");
			}
			out.println("");
		}
		out.close();
	}

	public static long gcd(long a, long b){
		if(a > b)
			a = (a+b)-(b=a);
		if(a == 0L)
			return b;
		return gcd(b%a, a);
	}

	public static boolean isPrime(long n){
		if(n < 2) return false;
		if(n == 2 || n == 3) return true;
		if(n%2 == 0 || n%3 == 0) return false;
		long sqrtN = (long)Math.sqrt(n)+1;
		for(long i = 6L; i <= sqrtN; i += 6) {
			if(n%(i-1) == 0 || n%(i+1) == 0) return false;
		}
		return true;
	}

	public static ArrayList<Integer> findDiv(int N){
		//gens all divisors of N
		ArrayList<Integer> ls1 = new ArrayList<Integer>();
		ArrayList<Integer> ls2 = new ArrayList<Integer>();
		for(int i=1; i <= (int)(Math.sqrt(N)+0.00000001); i++)
			if(N%i == 0)
			{
				ls1.add(i);
				ls2.add(N/i);
			}
		Collections.reverse(ls2);
		for(int b: ls2)
			if(b != ls1.get(ls1.size()-1))
				ls1.add(b);
		return ls1;
	}

	public static long power(long x, long y, long p){
		//0^0 = 1
		long res = 1L;
		x = x%p;
		while(y > 0)
		{
			if((y&1)==1)
				res = (res*x)%p;
			y >>= 1;
		x = (x*x)%p;
		}
		return res;
	}

	public static void printintarr(int[] arr) {
		for(int i = 0; i < arr.length; i++) {
			System.out.print(arr[i]+" ");
		}
	}

	public static void printlongarr(long[] arr) {
		for(int i = 0; i < arr.length; i++) {
			System.out.print(arr[i]+" ");
		}
	}

	public static void printdoublearr(double[] arr) {
		for(int i = 0; i < arr.length; i++) {
			System.out.print(arr[i]+" ");
		}
	}

	public static void printintarr(int arr[][]) {
		for(int i = 0 ; i < arr.length; i++) {
			for(int j = 0; j < arr[0].length; j++) {
				System.out.print(arr[i][j]+" ");
			}
			System.out.println();
		}
	}

	public static void printlongarr(long arr[][]) {
		for(int i = 0 ; i < arr.length; i++) {
			for(int j = 0; j < arr[0].length; j++) {
				System.out.print(arr[i][j]+" ");
			}
			System.out.println();
		}
	}

	public static void printdoublearr(double arr[][]) {
		for(int i = 0 ; i < arr.length; i++) {
			for(int j = 0; j < arr[0].length; j++) {
				System.out.print(arr[i][j]+" ");
			}
			System.out.println();
		}
	}

	public static void takeintarr(int arr[]) {
		for(int i = 0; i < arr.length; i++) {
			arr[i] = s.nextInt();
		}
	}

	public static void takeintarr(int arr[][]) {
		for(int i = 0 ; i < arr.length; i++) {
			for(int j = 0; j < arr[0].length; j++) {
				arr[i][j] = s.nextInt();
			}
		}
	}
}