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;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
import java.io.PrintWriter;
public class codeforces {
	public static void main(String[] args) {
		FastScanner s=new FastScanner();
		PrintWriter out=new PrintWriter(System.out);
		int t=s.nextInt();
		for(int tt=0;tt<t;tt++) {
			int a=s.nextInt(),b=s.nextInt();
			ArrayList<Integer> ans=new ArrayList<>();
			if(a<b) {
				int temp=a;
				a=b;
				b=temp;
			}
			if(a==b) {
				for(int i=0;i<=a+b;i+=2) {
					ans.add(i);
				}
			}else if(b==0) {
				if(a%2==0) {
					ans.add(a/2);
				}else {
					ans.add(a/2);
					ans.add((a+1)/2);
				}
			}else {
				if((b-a)%2==0) {
					for(int i=(a-b)/2;i<=a+2*b-(a+1)/2;i+=2) {
						ans.add(i);
					}
				}else {
					for(int i=(a-b)/2;i<=a+2*b-(a+1)/2;i++) {
						ans.add(i);
					}
				}
				
			}
			out.println(ans.size());
			for(int i:ans) {
				out.print(i+" ");
			}
			out.println();
		}
		out.close();
	}
	static boolean isPrime(int 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 void sort(long [] a) {
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
    static void sort(int [] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
    static int gcd(int a, int b){
      if (b == 0)
        return a;
      return gcd(b, a % b);
    }
    static void sortcol(int a[][],int c) {
		Arrays.sort(a, (x, y) -> {
			if(x[c]>y[c]) {
				return 1;
			}else {
				return -1;
			}
		});
	}
    public static void printb(boolean ans) {
    	if(ans) {
    		System.out.println("Yes");
    	}else {
    		System.out.println("No");
    	}
    }
    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();
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		boolean nextBoolean() {
			return Boolean.parseBoolean(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());
		}
		long[] readArrayLong(int n) {
			long[] a=new long[n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
	}
	
}
class Pair implements Comparable<Pair>{
	int a , b; 
	Pair(int x , int y){
		a=x;
		b=y;
	}
	public int compareTo(Pair o) {
		if(a!=o.a) {
			return  a - o.a;
		}
		return  b - o.b;
	}
}
