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.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.Collection;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        BCharmedByTheGame solver = new BCharmedByTheGame();
        solver.solve(1, in, out);
        out.close();
    }

    static class BCharmedByTheGame {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int tc = in.nextInt();
            for (int i = 0; i < tc; i++) {
                int a = in.nextInt();
                int b = in.nextInt();

                int totalGames = a + b;
                int h = totalGames / 2;

                EzIntSortedSet ez = new EzIntTreeSet();
                // how many ways are there of distributing p

                //int h or h + 1 = breaks away from you
                h += totalGames % 2;

                // b serves first, a has max h breaks;
                for (int x = 0; x < 2; x++) {
                    int mina = 0;
                    int maxa = 0;
                    if (a < h) {
                        mina = 0;
                        maxa = a;
                    }

                    if (a >= h) {
                        mina = a - (totalGames - h);
                        maxa = h;
                    }

                    for (int j = mina; j <= maxa; j++) {
                        int bonb = h - j;
                        int totalbreaks = b - bonb + j;
                        ez.add(totalbreaks);
                    }
                    int tmp = b;
                    b = a;
                    a = tmp;
                }
                out.println(ez.size());
                out.println(ez.toArray());
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static interface EzIntSortedSet extends EzIntSet {
        int size();

        EzIntIterator iterator();

        int[] toArray();

        boolean add(int element);

        boolean equals(Object object);

        int hashCode();

        String toString();

    }

    static interface EzIntCollection {
        int size();

        EzIntIterator iterator();

        boolean equals(Object object);

        int hashCode();

        String toString();

    }

    static class EzIntTreeSet implements EzIntSortedSet {
        private static final int DEFAULT_CAPACITY = 10;
        private static final double ENLARGE_SCALE = 2.0;
        private static final int HASHCODE_INITIAL_VALUE = 0x811c9dc5;
        private static final int HASHCODE_MULTIPLIER = 0x01000193;
        private static final boolean BLACK = false;
        private static final boolean RED = true;
        private static final int NULL = 0;
        private int[] key;
        private int[] left;
        private int[] right;
        private int[] p;
        private boolean[] color;
        private int size;
        private int root;
        private boolean returnedNull;

        public EzIntTreeSet() {
            this(DEFAULT_CAPACITY);
        }

        public EzIntTreeSet(int capacity) {
            if (capacity < 0) {
                throw new IllegalArgumentException("Capacity must be non-negative");
            }
            capacity++;
            key = new int[capacity];
            left = new int[capacity];
            right = new int[capacity];
            p = new int[capacity];
            color = new boolean[capacity];
            color[NULL] = BLACK;
            size = 0;
            root = NULL;
            returnedNull = false;
        }

        public EzIntTreeSet(EzIntCollection collection) {
            this(collection.size());
            for (EzIntIterator iterator = collection.iterator(); iterator.hasNext(); ) {
                add(iterator.next());
            }
        }

        public EzIntTreeSet(int[] srcArray) {
            this(srcArray.length);
            for (int element : srcArray) {
                add(element);
            }
        }

        public EzIntTreeSet(Collection<Integer> javaCollection) {
            this(javaCollection.size());
            for (int element : javaCollection) {
                add(element);
            }
        }

        public int size() {
            return size;
        }

        public EzIntIterator iterator() {
            return new EzIntTreeSetIterator();
        }

        public int[] toArray() {
            int[] result = new int[size];
            for (int i = 0, x = firstNode(); x != NULL; x = successorNode(x), i++) {
                result[i] = key[x];
            }
            return result;
        }

        public boolean add(int element) {
            int y = NULL;
            int x = root;
            while (x != NULL) {
                //noinspection SuspiciousNameCombination
                y = x;
                if (element < key[x]) {
                    x = left[x];
                } else if (element > key[x]) {
                    x = right[x];
                } else {
                    return false;
                }
            }
            if (size == color.length - 1) {
                enlarge();
            }
            int z = ++size;
            key[z] = element;
            p[z] = y;
            if (y == NULL) {
                root = z;
            } else {
                if (element < key[y]) {
                    left[y] = z;
                } else {
                    right[y] = z;
                }
            }
            left[z] = NULL;
            right[z] = NULL;
            color[z] = RED;
            fixAfterAdd(z);
            return true;
        }

        private int successorNode(int x) {
            if (right[x] != NULL) {
                x = right[x];
                while (left[x] != NULL) {
                    x = left[x];
                }
                return x;
            } else {
                int y = p[x];
                while (y != NULL && x == right[y]) {
                    //noinspection SuspiciousNameCombination
                    x = y;
                    y = p[y];
                }
                return y;
            }
        }

        private void fixAfterAdd(int z) {
            while (color[p[z]] == RED) {
                if (p[z] == left[p[p[z]]]) {
                    int y = right[p[p[z]]];
                    if (color[y] == RED) {
                        color[p[z]] = BLACK;
                        color[y] = BLACK;
                        color[p[p[z]]] = RED;
                        z = p[p[z]];
                    } else {
                        if (z == right[p[z]]) {
                            z = p[z];
                            rotateLeft(z);
                        }
                        color[p[z]] = BLACK;
                        color[p[p[z]]] = RED;
                        rotateRight(p[p[z]]);
                    }
                } else {
                    int y = left[p[p[z]]];
                    if (color[y] == RED) {
                        color[p[z]] = BLACK;
                        color[y] = BLACK;
                        color[p[p[z]]] = RED;
                        z = p[p[z]];
                    } else {
                        if (z == left[p[z]]) {
                            z = p[z];
                            rotateRight(z);
                        }
                        color[p[z]] = BLACK;
                        color[p[p[z]]] = RED;
                        rotateLeft(p[p[z]]);
                    }
                }
            }
            color[root] = BLACK;
        }

        private void rotateLeft(int x) {
            int y = right[x];
            right[x] = left[y];
            if (left[y] != NULL) {
                p[left[y]] = x;
            }
            p[y] = p[x];
            if (p[x] == NULL) {
                root = y;
            } else {
                if (x == left[p[x]]) {
                    left[p[x]] = y;
                } else {
                    right[p[x]] = y;
                }
            }
            left[y] = x;
            p[x] = y;
        }

        private void rotateRight(int x) {
            int y = left[x];
            left[x] = right[y];
            if (right[y] != NULL) {
                p[right[y]] = x;
            }
            p[y] = p[x];
            if (p[x] == NULL) {
                root = y;
            } else {
                if (x == right[p[x]]) {
                    right[p[x]] = y;
                } else {
                    left[p[x]] = y;
                }
            }
            right[y] = x;
            p[x] = y;
        }

        private void enlarge() {
            int newLength = Math.max(color.length + 1, (int) (color.length * ENLARGE_SCALE));
            key = Arrays.copyOf(key, newLength);
            left = Arrays.copyOf(left, newLength);
            right = Arrays.copyOf(right, newLength);
            p = Arrays.copyOf(p, newLength);
            color = Arrays.copyOf(color, newLength);
        }

        private int firstNode() {
            int x = root;
            while (left[x] != NULL) {
                x = left[x];
            }
            return x;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            EzIntTreeSet that = (EzIntTreeSet) o;

            if (size != that.size) {
                return false;
            }
            for (int x = firstNode(), y = that.firstNode();
                 x != NULL;
                //noinspection SuspiciousNameCombination
                 x = successorNode(x), y = that.successorNode(y)
            ) {
                if (key[x] != that.key[y]) {
                    return false;
                }
            }
            return true;
        }

        public int hashCode() {
            int hash = HASHCODE_INITIAL_VALUE;
            for (int x = firstNode(); x != NULL; x = successorNode(x)) {
                hash = (hash ^ PrimitiveHashCalculator.getHash(key[x])) * HASHCODE_MULTIPLIER;
            }
            return hash;
        }

        public String toString() {
            StringBuilder sb = new StringBuilder();
            sb.append('[');
            for (int x = firstNode(); x != NULL; x = successorNode(x)) {
                if (sb.length() > 1) {
                    sb.append(", ");
                }
                sb.append(key[x]);
            }
            sb.append(']');
            return sb.toString();
        }

        private class EzIntTreeSetIterator implements EzIntIterator {
            private int x;

            private EzIntTreeSetIterator() {
                x = firstNode();
            }

            public boolean hasNext() {
                return x != NULL;
            }

            public int next() {
                if (x == NULL) {
                    throw new NoSuchElementException("Iterator doesn't have more elements");
                }
                final int result = key[x];
                x = successorNode(x);
                return result;
            }

        }

    }

    static interface EzIntIterator {
        boolean hasNext();

        int next();

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void println(int[] array) {
            print(array);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }

    static final class PrimitiveHashCalculator {
        private PrimitiveHashCalculator() {
        }

        public static int getHash(int x) {
            return x;
        }

    }

    static interface EzIntSet extends EzIntCollection {
        int size();

        EzIntIterator iterator();

        boolean equals(Object object);

        int hashCode();

        String toString();

    }
}

