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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    public static void main(String[] args){
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        solve(in, out);
        out.close();
    }

    static String reverse(String s) {
        return (new StringBuilder(s)).reverse().toString();
    }

    static void sieveOfEratosthenes(int n, int factors[], ArrayList<Integer> ar) 
    { 
        factors[1]=1;
        int p;
        for(p = 2; p*p <=n; p++) 
        { 
            if(factors[p] == 0) 
            { 
                ar.add(p);
                factors[p]=p;
                for(int i = p*p; i <= n; i += p) 
                    if(factors[i]==0)
                        factors[i] = p; 
            } 
        } 
        for(;p<=n;p++){
            if(factors[p] == 0) 
            { 
                factors[p] = p;
                ar.add(p);
            } 
        }
    }

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

    static void sort1(long ar[]) {
        int n = ar.length;
        ArrayList<Long> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static void sort2(char ar[]) {
        int n = ar.length;
        ArrayList<Character> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static long ncr(long n, long r, long mod) {
        if (r == 0)
            return 1;
        long val = ncr(n - 1, r - 1, mod);
        val = (n * val) % mod;
        val = (val * modInverse(r, mod)) % mod;
        return val;
    }

    // static long gcd[];
    
    // static void build(long a[], int v, int tl, int tr) {
    //     if (tl == tr) {
    //         gcd[v] = a[tl];
            
    //     } else {
    //         int tm = (tl + tr) / 2;
    //         build(a, v*2, tl, tm);
    //         build(a, v*2+1, tm+1, tr);
    //         gcd[v] = gcd(gcd[v*2], gcd[v*2+1]);
    //     }
    // }

    // static void push(int v, int tl, int tr){
    //     if(tl==tr){
    //         lz[v] = 0;
    //         return;
    //     }
    //     min[2*v] += lz[v];
    //     min[2*v+1] += lz[v];
    //     lz[2*v] += lz[v];
    //     lz[2*v+1] += lz[v];
    //     lz[v] = 0;
    // }

    // static void update(int v, int tl, int tr, int l, int r, int val) {
    //     push(v,tl,tr);
    //     if(tl>r||tr<l)
    //         return;
    //     if(tl>=l&&tr<=r){
    //         min[v] += val;
    //         lz[v] += val;
    //         return;
    //     }
    //     int tm = (tl + tr) / 2;
    //     update(v*2, tl, tm, l, r, val);
    //     update(v*2+1, tm+1, tr, l, r, val);
    //     min[v] = Math.min(min[2*v],min[2*v+1]);
    // }

    // static long get(int v, int tl, int tr, int l, int r) {
    //     if (tl >= l && tr <= r) {
    //         return gcd[v];
    //     }
    //     int tm = (tl + tr) / 2;
    //     if(l>tm){
    //         return get(2*v+1, tm+1, tr, l, r);
    //     }
    //     if(r<tm+1){
    //         return get(2*v, tl, tm, l, r);
    //     }
    //     return gcd(get(2*v, tl, tm, l, r), get(2*v+1, tm+1, tr, l, r));
    // }

    // static int y = 0;

    static int parent[];
    static int rank[];

    static int find_set(int v) {
        if (v == parent[v])
            return v;
        return find_set(parent[v]);
    }
    
    static void make_set(int v) {
        parent[v] = v;
        rank[v] = 0;
    }
    
    static void union_sets(int a, int b) {
        a = find_set(a);
        b = find_set(b);
        if (a != b) {
            if (rank[a] < rank[b]){
                int tmp = a;
                a = b;
                b = tmp;
            }
            parent[b] = a;
            if (rank[a] == rank[b])
                rank[a]++;
        }
    }

    static int parent1[];
    static int rank1[];

    static int find_set1(int v) {
        if (v == parent1[v])
            return v;
        return find_set1(parent1[v]);
    }
    
    static void make_set1(int v) {
        parent1[v] = v;
        rank1[v] = 0;
    }
    
    static void union_sets1(int a, int b) {
        a = find_set1(a);
        b = find_set1(b);
        if (a != b) {
            if (rank1[a] < rank1[b]){
                int tmp = a;
                a = b;
                b = tmp;
            }
            parent1[b] = a;
            if (rank1[a] == rank1[b])
                rank1[a]++;
        }
    }

    public static void solve(InputReader sc, PrintWriter pw){
        int i, j = 0;
        // int t = 1; 
        long mod = 1000000007;
        int t = sc.nextInt();
        u: while (t-- > 0) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            if(a<b){
                int tmp = a;
                a = b;
                b = tmp;
            }
            int c[] = new int[a+b];
            int n = a+b;
            int x = a;
            for(i=0;i<n&&x>0;i+=2){
                c[i] = 1;
                x--;
            }
            for(i=1;i<n&&x>0;i+=2){
                c[i] = 1;
                x--;
            }
            int max = 0, min = 0;
            ArrayList<Integer> ar = new ArrayList<>();
            for(i=0;i<n;i++){
                if(c[i]==i%2){
                    max++;
                }
                else{
                    min++;
                }
            }
            if(max<min){
                int tmp = max;
                max = min;
                min = tmp;
            }
            ar.add(max);
            ar.add(min);
            for(i=min+2;i<max;i+=2){
                ar.add(i);
            }
            for(i=max-2;i>min;i-=2){
                ar.add(i);
            }
            Collections.sort(ar);
            int last = -1;
            ArrayList<Integer> ar1 = new ArrayList<>();
            for(i=0;i<ar.size();i++){
                if(ar.get(i)!=last){
                    last = ar.get(i);
                    ar1.add(last);
                }
            }
            pw.println(ar1.size());
            for(int y:ar1){
                pw.print(y+" ");
            }
            pw.println();
        }
    }


    static void KMPSearch(char pat[], char txt[], int pres[])
    {
        int M = pat.length;
        int N = txt.length;
        int lps[] = new int[M];
        int j = 0; 
        computeLPSArray(pat, M, lps);
        int i = 0;
        while (i < N) {
            if (pat[j] == txt[i]) {
                j++;
                i++;
            }
            if (j == M) {
                pres[i-1] = 1;
                j = lps[j - 1];
            }
            else if (i < N && pat[j] != txt[i]) {
                if (j != 0)
                    j = lps[j - 1];
                else
                    i = i + 1;
            }
        }
    }
  
    static void computeLPSArray(char pat[], int M, int lps[])
    {
        int len = 0;
        int i = 1;
        lps[0] = 0; 
        while (i < M) {
            if (pat[i] == pat[len]) {
                len++;
                lps[i] = len;
                i++;
            }
            else 
            {
                if (len != 0) {
                    len = lps[len - 1];
                }
                else
                {
                    lps[i] = len;
                    i++;
                }
            }
        }
    }

    static long[][] matrixMult(long a[][], long b[][], long mod){
        int n = a.length;
        int m = a[0].length;
        int p = b[0].length;
        long c[][] = new long[n][p];
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                for(int k=0;k<p;k++){
                    c[i][k] += a[i][j]*b[j][k];
                    c[i][k] %= mod;
                }
            }
        }
        return c;
    }

    static long[][] exp(long mat[][], long b, long mod){
        if(b==0){
            int n = mat.length;
            long res[][] = new long[n][n];
            for(int i=0;i<n;i++){
                res[i][i] = 1;
            }
            return res;
        }
        long half[][] = exp(mat, b/2, mod);
        long res[][] = matrixMult(half, half, mod);
        if(b%2==1){
            res = matrixMult(res, mat, mod);
        }
        return res;
    }

    static void countPrimeFactors(int num, int a[], HashMap<Integer,Integer> pos){
        for(int i=2;i*i<num;i++){
            if(num%i==0){
                int y = pos.get(i);
                while(num%i==0){
                    a[y]++;
                    num/=i;
                }
            }
        }
        if(num>1){
            int y = pos.get(num);
            a[y]++;
        }
    }

    static void assignAnc(ArrayList<Integer> ar[], int depth[], int sz[], int par[][] ,int curr, int parent, int d){
        depth[curr] = d;
        sz[curr] = 1;
        par[curr][0] = parent;
        for(int v:ar[curr]){
            if(parent==v)
                continue;
            assignAnc(ar, depth, sz, par, v, curr, d+1);
            sz[curr] += sz[v];
        }
    }

    static int findLCA(int a, int b, int par[][], int depth[]){
        if(depth[a]>depth[b]){
            a = a^b;
            b = a^b;
            a = a^b;
        }
        int diff = depth[b] - depth[a];
        for(int i=19;i>=0;i--){
            if((diff&(1<<i))>0){
                b = par[b][i];
            }
        }
        if(a==b)
            return a;
        for(int i=19;i>=0;i--){
            if(par[b][i]!=par[a][i]){
                b = par[b][i];
                a = par[a][i];
            }
        }
        return par[a][0];
    }

    static void formArrayForBinaryLifting(int n, int par[][]){
        for(int j=1;j<20;j++){
            for(int i=0;i<n;i++){
                if(par[i][j-1]==-1)
                    continue;
                par[i][j] = par[par[i][j-1]][j-1];
            }
        }
    }

    static long lcm(int a, int b){
        return a*b/gcd(a,b);
    }

    static class Pair1 {
        long a;
        long b;
        
        Pair1(long a, long b) {
            this.a = a;
            this.b = b;
        }
    }

    static class Pair implements Comparable<Pair> {
        int a;
        int b;
        // int c;
        
        Pair(int a, int b) {
            this.a = a;
            this.b = b;
            // this.c = c;
        }
 
        public int compareTo(Pair p) {
            // if(c!=p.c)
            return a-p.a;
            // return b-p.b;
        }
    }

    static class Pair2 implements Comparable<Pair2> {
        int a;
        int b;
        int c;
        
        Pair2(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }
 
        public int compareTo(Pair2 p) {
            return a-p.a;
        }
    }

    static boolean isPrime(int n) { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 ||  n % 3 == 0) 
            return false; 
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
                return false; 
        return true; 
    } 

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

    static long fast_pow(long base, long n, long M) {
        if (n == 0)
            return 1;
        if (n == 1)
            return base % M;
        long halfn = fast_pow(base, n / 2, M);
        if (n % 2 == 0)
            return (halfn * halfn) % M;
        else
            return (((halfn * halfn) % M) * base) % M;
    }

    static long modInverse(long n, long M) {
        return fast_pow(n, M - 2, M);
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 9992768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}