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.util.*;
import java.io.*;
import java.lang.*;
import java.math.BigInteger;

public class A {

	static FastReader		sc	= new FastReader();
	static PrintWriter	out	= new PrintWriter(System.out);


	public static void main(String[] args) throws Exception {

		int t = sc.ni();
		while (t-- > 0) {
			A.go();
		}
		out.flush();

	}

	// >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Code Starts <<<<<<<<<<<<<<<<<<<<<<<<<<<<< //

static void go() {
	int a=sc.ni(),b=sc.ni();
	int m=a+b;
	if(a<b) {
		int temp=b;
		b=a;
		a=temp;
	}
	ArrayList<Integer> ans=new ArrayList<>();
	if(a==b) {
		for(int i=0;i<=m;i+=2) {
			ans.add(i);
		}
		out.println(ans.size());
		for(int i:ans) {
			out.print(i+" ");
		}
		out.println();
		return;
	}
	if(b+1==a) {
		for(int i=0;i<=m;i+=1) {
			ans.add(i);
		}
		out.println(ans.size());
		for(int i:ans) {
			out.print(i+" ");
		}
		out.println();
		return;
	}
	if(b==0) {

		if(m/2==(m+1)/2) {
			out.println(1);
			out.println(m/2);
		}else {
			out.println(2);
			out.println(m/2+" "+(m+1)/2);
		}
		return;
	}
	for(int i=0;i<=m;i++) {
		if(check(i,(m+1)/2,m/2,m,a,b)) {
			ans.add(i);
			break;
		}
	}
	for(int i=ans.get(0)+2;i<=a;i+=2) {
		ans.add(i);
	}
	out.println(ans.size());
	for(int i:ans) {
		out.print(i+" ");
	}
	out.println();
	
}
static boolean check(int i,int a,int b,int m,int aa,int bb) {
	if(((a-i)==bb && b+i==aa)) {
		return true;
	}

	return false;
}

	// >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Code Ends <<<<<<<<<<<<<<<<<<<<<<<<<<<<< //
	static long	fact[];
	static long	invfact[];

	static long ncr(int n, int k) {
		if (k < 0 || k > n) {
			return 0;
		}
		long x = fact[n] % mod;
		long y = invfact[k] % mod;
		long yy = invfact[n - k] % mod;
		long ans = (x * y) % mod;
		ans = (ans * yy) % mod;
		return ans;
	}

	static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	static int	prime[]	= new int[200005];
	static int	N				= 200005;

	static void sieve() {

		for (int i = 0; i < N; i++) {
			prime[i] = i;
		}
		for (int i = 2; i * i <= N; i++) {
			if (prime[i] == i) {
				prime[i] = i;
				for (int j = i; j < N; j += i) {
					prime[j] = i;
				}
			}
		}
	}

	static int gcd(int a, int b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	static void sort(int[] a) {
		ArrayList<Integer> aa = new ArrayList<>();
		for (Integer i : a) {
			aa.add(i);
		}
		Collections.sort(aa);
		for (int i = 0; i < a.length; i++)
			a[i] = aa.get(i);
	}

	static void sort(long[] a) {
		ArrayList<Long> aa = new ArrayList<>();
		for (Long i : a) {
			aa.add(i);
		}
		Collections.sort(aa);
		for (int i = 0; i < a.length; i++)
			a[i] = aa.get(i);
	}

	static int mod = (int) 1000000007;

	static long pow(long x, long y) {
		long res = 1l;
		while (y != 0) {
			if (y % 2 == 1) {
				res = (x % mod * res % mod) % mod;
			}
			y /= 2;
			x = (x % mod * x % mod) % mod;
		}
		return res % mod;
	}

	// >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Fast IO <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< //

	static class FastReader {
		BufferedReader	br;
		StringTokenizer	st;

		public FastReader() {
			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 ni() {
			return Integer.parseInt(next());
		}

		long nl() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		int[] intArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = sc.ni();
			return a;
		}

		long[] longArray(int n) {
			long a[] = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = sc.nl();
			return a;
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
}
