Problem: Now Vasya is taking an exam in mathematics. In order to get a good mark, Vasya needs to guess the matrix that the teacher has constructed!

Vasya knows that the matrix consists of n rows and m columns. For each row, he knows the xor (bitwise excluding or) of the elements in this row. The sequence a1, a2, ..., an denotes the xor of elements in rows with indices 1, 2, ..., n, respectively. Similarly, for each column, he knows the xor of the elements in this column. The sequence b1, b2, ..., bm denotes the xor of elements in columns with indices 1, 2, ..., m, respectively.

Help Vasya! Find a matrix satisfying the given constraints or tell him that there is no suitable matrix.

Input

The first line contains two numbers n and m (2 ≤ n, m ≤ 100) — the dimensions of the matrix.

The second line contains n numbers a1, a2, ..., an (0 ≤ ai ≤ 109), where ai is the xor of all elements in row i.

The third line contains m numbers b1, b2, ..., bm (0 ≤ bi ≤ 109), where bi is the xor of all elements in column i.

Output

If there is no matrix satisfying the given constraints in the first line, output "NO".

Otherwise, on the first line output "YES", and then n rows of m numbers in each ci1, ci2, ... , cim (0 ≤ cij ≤ 2·109) — the description of the matrix.

If there are several suitable matrices, it is allowed to print any of them.

Examples

Input

2 3
2 9
5 3 13


Output

YES
3 4 5
6 7 8


Input

3 3
1 7 6
2 15 12


Output

NO

Solution (in JAVA):

Solution:
import java.awt.*;
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
import java.util.List;

import static java.lang.Math.max;
import static java.lang.Math.min;


public class D implements Runnable{

    // SOLUTION AT THE TOP OF CODE!!!
    // HACK ME PLEASE IF YOU CAN!!!
    // PLEASE!!!
    // PLEASE!!!
    // PLEASE!!!

    @SuppressWarnings("unused")
    private final static Random rnd = new Random();
    private final static String fileName = "";

    private final static long MODULO = 1000 * 1000 * 1000 + 7;

    // THERE SOLUTION STARTS!!!
    private void solve() {
        int n = readInt();
        int m = readInt();

        int[] a = readIntArray(n);
        int[] b = readIntArray(m);

        int aXor = 0;
        for (int i = 0; i < n - 1; ++i) {
            aXor ^= a[i];
        }

        int bXor = 0;
        for (int j = 0; j < m - 1; ++j) {
            bXor ^= b[j];
        }

        int rowValue = bXor ^ a[n - 1];
        int columnValue = aXor ^ b[m - 1];

        if (rowValue == columnValue) {
            yesNo(true);
            for (int i = 0; i < n - 1; ++i) {
                for (int j = 0; j < m - 1; ++j) out.print("0 ");
                out.println(a[i]);
            }

            for (int j = 0; j < m - 1; ++j) out.print(b[j] + " ");
            out.println(rowValue);
        } else {
            yesNo(false);
        }
    }

    /////////////////////////////////////////////////////////////////////

    private final static boolean MULTIPLE_TESTS = true;
    private final boolean ONLINE_JUDGE = !new File("input.txt").exists();
//    private final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    private final static int MAX_STACK_SIZE = 128;

    private final static boolean OPTIMIZE_READ_NUMBERS = false;

    /////////////////////////////////////////////////////////////////////

    @SuppressWarnings("unused")
    private static long inverse(long x) {
        return binpow(x, MODULO - 2);
    }

    private static long binpow(long base, long power) {
        if (power == 0) return 1;
        if ((power & 1) == 0) {
            long half = binpow(base, power >> 1);
            return mult(half, half);
        } else {
            long prev = binpow(base, power - 1);
            return mult(prev, base);
        }
    }

    private static long add(long a, long b) { return (a + b) % MODULO; }

    @SuppressWarnings("unused")
    private static long subtract(long a, long b) { return add(a, MODULO - b % MODULO); }

    private static long mult(long a, long b) { return (a * b) % MODULO; }

    /////////////////////////////////////////////////////////////////////

    @SuppressWarnings("unused")
    void yesNo(boolean yes) {
        out.println(yes ? "YES" : "NO");
    }

    /////////////////////////////////////////////////////////////////////

    public void run(){
        try{
            timeInit();
            Locale.setDefault(Locale.US);

            init();

            if (ONLINE_JUDGE) {
                solve();
            } else {
                do {
                    try {
                        timeInit();
                        solve();
                        time();

                        out.println();
                        out.flush();
                    } catch (EOFException e) {
                        break;
                    }
                } while (MULTIPLE_TESTS);
            }

            out.close();
            time();
        }catch (Exception e){
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }

    /////////////////////////////////////////////////////////////////////

    private BufferedReader in;
    private OutputWriter out;
    private StringTokenizer tok = new StringTokenizer("");

    public static void main(String[] args){
        new Thread(null, new D(), "", MAX_STACK_SIZE * (1L << 20)).start();
    }

    /////////////////////////////////////////////////////////////////////

    private void init() throws FileNotFoundException{
        Locale.setDefault(Locale.US);

        if (ONLINE_JUDGE){
            if (fileName.isEmpty()) {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new OutputWriter(System.out);
            } else {
                in = new BufferedReader(new FileReader(fileName + ".in"));
                out = new OutputWriter(fileName + ".out");
            }
        }else{
            in = new BufferedReader(new FileReader("input.txt"));
            out = new OutputWriter("output.txt");
        }
    }

    ////////////////////////////////////////////////////////////////

    private long timeBegin;

    private void timeInit() {
        this.timeBegin = System.currentTimeMillis();
    }

    private void time(){
        long timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    @SuppressWarnings("unused")
    private void debug(Object... objects){
        if (ONLINE_JUDGE){
            for (Object o: objects){
                System.err.println(o.toString());
            }
        }
    }

    /////////////////////////////////////////////////////////////////////

    private String delim = " ";

    private String readNullableLine() {
        try {
            return in.readLine();
        } catch (IOException e) {
            throw new RuntimeIOException(e);
        }
    }

    private String readLine() {
        String line = readNullableLine();
        if (null == line) throw new EOFException();
        return line;
    }

    private String readString() {
        while(!tok.hasMoreTokens()){
            tok = new StringTokenizer(readLine(), delim);
        }

        return tok.nextToken(delim);
    }

    /////////////////////////////////////////////////////////////////

    private final char NOT_A_SYMBOL = '\0';

    @SuppressWarnings("unused")
    private char readChar() {
        try {
            int intValue = in.read();

            if (intValue == -1){
                return NOT_A_SYMBOL;
            }

            return (char) intValue;
        } catch (IOException e) {
            throw new RuntimeIOException(e);
        }
    }

    private char[] readCharArray() {
        return readLine().toCharArray();
    }

    @SuppressWarnings("unused")
    private char[][] readCharField(int rowsCount) {
        char[][] field = new char[rowsCount][];
        for (int row = 0; row < rowsCount; ++row) {
            field[row] = readCharArray();
        }

        return field;
    }

    /////////////////////////////////////////////////////////////////

    private long optimizedReadLong() {
        int sign = 1;
        long result = 0;
        boolean started = false;
        while (true) {
            try {
                int j = in.read();
                if (-1 == j) {
                    if (started) return sign * result;
                    throw new NumberFormatException();
                }

                if (j == '-') {
                    if (started) throw new NumberFormatException();
                    sign = -sign;
                }

                if ('0' <= j && j <= '9') {
                    result = result * 10 + j - '0';
                    started = true;
                } else if (started) {
                    return sign * result;
                }
            } catch (IOException e) {
                throw new RuntimeIOException(e);
            }
        }
    }

    private int readInt() {

        if (!OPTIMIZE_READ_NUMBERS) {
            return Integer.parseInt(readString());
        } else {
            return (int) optimizedReadLong();
        }
    }

    private int[] readIntArray(int size) {
        int[] array = new int[size];

        for (int index = 0; index < size; ++index){
            array[index] = readInt();
        }

        return array;
    }

    @SuppressWarnings("unused")
    private int[] readSortedIntArray(int size) {
        Integer[] array = new Integer[size];

        for (int index = 0; index < size; ++index) {
            array[index] = readInt();
        }
        Arrays.sort(array);

        int[] sortedArray = new int[size];
        for (int index = 0; index < size; ++index) {
            sortedArray[index] = array[index];
        }

        return sortedArray;
    }

    private int[] readIntArrayWithDecrease(int size) {
        int[] array = readIntArray(size);

        for (int i = 0; i < size; ++i) {
            array[i]--;
        }

        return array;
    }

    ///////////////////////////////////////////////////////////////////

    @SuppressWarnings("unused")
    private int[][] readIntMatrix(int rowsCount, int columnsCount) {
        int[][] matrix = new int[rowsCount][];

        for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
            matrix[rowIndex] = readIntArray(columnsCount);
        }

        return matrix;
    }

    @SuppressWarnings("unused")
    private int[][] readIntMatrixWithDecrease(int rowsCount, int columnsCount) {
        int[][] matrix = new int[rowsCount][];

        for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
            matrix[rowIndex] = readIntArrayWithDecrease(columnsCount);
        }

        return matrix;
    }

    ///////////////////////////////////////////////////////////////////

    private long readLong() {
        if (!OPTIMIZE_READ_NUMBERS) {
            return Long.parseLong(readString());
        } else {
            return optimizedReadLong();
        }
    }

    @SuppressWarnings("unused")
    private long[] readLongArray(int size) {
        long[] array = new long[size];

        for (int index = 0; index < size; ++index){
            array[index] = readLong();
        }

        return array;
    }

    ////////////////////////////////////////////////////////////////////

    private double readDouble() {
        return Double.parseDouble(readString());
    }

    @SuppressWarnings("unused")
    private double[] readDoubleArray(int size) {
        double[] array = new double[size];

        for (int index = 0; index < size; ++index){
            array[index] = readDouble();
        }

        return array;
    }

    ////////////////////////////////////////////////////////////////////

    @SuppressWarnings("unused")
    private BigInteger readBigInteger() {
        return new BigInteger(readString());
    }

    @SuppressWarnings("unused")
    private BigDecimal readBigDecimal() {
        return new BigDecimal(readString());
    }

    /////////////////////////////////////////////////////////////////////

    private Point readPoint() {
        int x = readInt();
        int y = readInt();
        return new Point(x, y);
    }

    @SuppressWarnings("unused")
    private Point[] readPointArray(int size) {
        Point[] array = new Point[size];

        for (int index = 0; index < size; ++index){
            array[index] = readPoint();
        }

        return array;
    }

    /////////////////////////////////////////////////////////////////////

    @Deprecated
    @SuppressWarnings("unused")
    private List<Integer>[] readGraph(int vertexNumber, int edgeNumber) {
        @SuppressWarnings("unchecked")
        List<Integer>[] graph = new List[vertexNumber];

        for (int index = 0; index < vertexNumber; ++index){
            graph[index] = new ArrayList<>();
        }

        while (edgeNumber-- > 0){
            int from = readInt() - 1;
            int to = readInt() - 1;

            graph[from].add(to);
            graph[to].add(from);
        }

        return graph;
    }

    private static class GraphBuilder {

        final int size;
        final List<Integer>[] edges;

        static GraphBuilder createInstance(int size) {
            @SuppressWarnings("unchecked")
            List<Integer>[] edges = new List[size];
            for (int v = 0; v < size; ++v) {
                edges[v] = new ArrayList<>();
            }

            return new GraphBuilder(edges);
        }

        private GraphBuilder(List<Integer>[] edges) {
            this.size = edges.length;
            this.edges = edges;
        }

        public void addEdge(int from, int to) {
            addDirectedEdge(from, to);
            addDirectedEdge(to, from);
        }

        public void addDirectedEdge(int from, int to) {
            edges[from].add(to);
        }

        public int[][] build() {
            int[][] graph = new int[size][];
            for (int v = 0; v < size; ++v) {
                List<Integer> vEdges = edges[v];
                graph[v] = castInt(vEdges);
            }

            return graph;
        }
    }

    @SuppressWarnings("unused")
    private final static int ZERO_INDEXATION = 0, ONE_INDEXATION = 1;

    @SuppressWarnings("unused")
    private int[][] readUnweightedGraph(int vertexNumber, int edgesNumber) {
        return readUnweightedGraph(vertexNumber, edgesNumber, ONE_INDEXATION, false);
    }

    private int[][] readUnweightedGraph(int vertexNumber, int edgesNumber,
                                        int indexation, boolean directed
    ) {
        GraphBuilder graphBuilder = GraphBuilder.createInstance(vertexNumber);
        for (int i = 0; i < edgesNumber; ++i) {
            int from = readInt() - indexation;
            int to = readInt() - indexation;

            if (directed) graphBuilder.addDirectedEdge(from, to);
            else graphBuilder.addEdge(from, to);
        }

        return graphBuilder.build();
    }

    private static class Edge {
        int to;
        int w;

        Edge(int to, int w) {
            this.to = to;
            this.w = w;
        }
    }

    @SuppressWarnings("unused")
    private Edge[][] readWeightedGraph(int vertexNumber, int edgesNumber) {
        return readWeightedGraph(vertexNumber, edgesNumber, ONE_INDEXATION, false);
    }

    private Edge[][] readWeightedGraph(int vertexNumber, int edgesNumber,
                                       int indexation, boolean directed) {
        @SuppressWarnings("unchecked")
        List<Edge>[] graph = new List[vertexNumber];
        for (int v = 0; v < vertexNumber; ++v) {
            graph[v] = new ArrayList<>();
        }

        while (edgesNumber --> 0) {
            int from = readInt() - indexation;
            int to = readInt() - indexation;
            int w = readInt();

            graph[from].add(new Edge(to, w));
            if (!directed) graph[to].add(new Edge(from, w));
        }

        Edge[][] graphArrays = new Edge[vertexNumber][];
        for (int v = 0; v < vertexNumber; ++v) {
            graphArrays[v] = graph[v].toArray(new Edge[0]);
        }

        return graphArrays;
    }

    /////////////////////////////////////////////////////////////////////

    private static class IntIndexPair {

        @SuppressWarnings("unused")
        static Comparator<IntIndexPair> increaseComparator = (indexPair1, indexPair2) -> {
            int value1 = indexPair1.value;
            int value2 = indexPair2.value;

            if (value1 != value2) return value1 - value2;

            int index1 = indexPair1.index;
            int index2 = indexPair2.index;

            return index1 - index2;
        };

        @SuppressWarnings("unused")
        static Comparator<IntIndexPair> decreaseComparator = (indexPair1, indexPair2) -> {
            int value1 = indexPair1.value;
            int value2 = indexPair2.value;

            if (value1 != value2) return -(value1 - value2);

            int index1 = indexPair1.index;
            int index2 = indexPair2.index;

            return index1 - index2;
        };

        @SuppressWarnings("unused")
        static IntIndexPair[] from(int[] array) {
            IntIndexPair[] iip = new IntIndexPair[array.length];
            for (int i = 0; i < array.length; ++i) {
                iip[i] = new IntIndexPair(array[i], i);
            }

            return iip;
        }

        int value, index;

        IntIndexPair(int value, int index) {
            super();
            this.value = value;
            this.index = index;
        }

        @SuppressWarnings("unused")
        int getRealIndex() {
            return index + 1;
        }
    }

    @SuppressWarnings("unused")
    private IntIndexPair[] readIntIndexArray(int size) {
        IntIndexPair[] array = new IntIndexPair[size];

        for (int index = 0; index < size; ++index) {
            array[index] = new IntIndexPair(readInt(), index);
        }

        return array;
    }

    /////////////////////////////////////////////////////////////////////

    private static class OutputWriter extends PrintWriter {

        final int DEFAULT_PRECISION = 12;

        private int precision;
        private String format, formatWithSpace;

        {
            precision = DEFAULT_PRECISION;

            format = createFormat(precision);
            formatWithSpace = format + " ";
        }

        OutputWriter(OutputStream out) {
            super(out);
        }

        OutputWriter(String fileName) throws FileNotFoundException {
            super(fileName);
        }

        int getPrecision() {
            return precision;
        }

        void setPrecision(int precision) {
            precision = max(0, precision);
            this.precision = precision;

            format = createFormat(precision);
            formatWithSpace = format + " ";
        }

        String createFormat(int precision){
            return "%." + precision + "f";
        }

        @Override
        public void print(double d){
            printf(format, d);
        }
        
        @Override
        public void println(double d){
            print(d);
            println();
        }

        void printWithSpace(double d){
            printf(formatWithSpace, d);
        }

        void printAll(double...d){
            for (int i = 0; i < d.length - 1; ++i){
                printWithSpace(d[i]);
            }

            print(d[d.length - 1]);
        }

        @SuppressWarnings("unused")
        void printlnAll(double... d){
            printAll(d);
            println();
        }
        
        void printAll(int... array) {
        	for (int value : array) {
        		print(value + " ");
        	}
        }

        @SuppressWarnings("unused")
        void printlnAll(int... array) {
        	printAll(array);
        	println();
        }
        
        void printAll(long... array) {
        	for (long value : array) {
        		print(value + " ");
        	}
        }

        @SuppressWarnings("unused")
        void printlnAll(long... array) {
        	printAll(array);
        	println();
        }
    }

    /////////////////////////////////////////////////////////////////////

    private static class EOFException extends RuntimeException {

        EOFException() {
            super();
        }
    }

    private static class RuntimeIOException extends RuntimeException {

        /**
         *
         */
        private static final long serialVersionUID = -6463830523020118289L;

        RuntimeIOException(Throwable cause) {
            super(cause);
        }
    }

    /////////////////////////////////////////////////////////////////////
    //////////////// Some useful constants andTo functions ////////////////
    /////////////////////////////////////////////////////////////////////

    private static void swap(int[] array, int i, int j) {
        if (i != j) {
            int tmp = array[i];
            array[i] = array[j];
            array[j] = tmp;
        }
    }

    private static final int[][] steps = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
    private static final int[][] steps8 = {
            {-1, 0}, {1, 0}, {0, -1}, {0, 1},
            {-1, -1}, {1, 1}, {1, -1}, {-1, 1}
    };

    @SuppressWarnings("unused")
    private static boolean checkCell(int row, int rowsCount, int column, int columnsCount) {
        return checkIndex(row, rowsCount) && checkIndex(column, columnsCount);
    }

    private static boolean checkIndex(int index, int lim){
        return (0 <= index && index < lim);
    }

    /////////////////////////////////////////////////////////////////////

    private static int getBit(long mask, int bit) { return (int)((mask >> bit) & 1); }

    @SuppressWarnings("unused")
    private static boolean checkBit(long mask, int bit){
        return getBit(mask, bit) != 0;
    }

    /////////////////////////////////////////////////////////////////////

    @SuppressWarnings("unused")
    private static long getSum(int[] array) {
        long sum = 0;
        for (int value: array) {
            sum += value;
        }

        return sum;
    }

    @SuppressWarnings("unused")
    private static Point getMinMax(int[] array) {
        int min = array[0];
        int max = array[0];

        for (int index = 0, size = array.length; index < size; ++index, ++index) {
            int value = array[index];

            if (index == size - 1) {
                min = min(min, value);
                max = max(max, value);
            } else {
                int otherValue = array[index + 1];

                if (value <= otherValue) {
                    min = min(min, value);
                    max = max(max, otherValue);
                } else {
                    min = min(min, otherValue);
                    max = max(max, value);
                }
            }
        }

        return new Point(min, max);
    }

    /////////////////////////////////////////////////////////////////////

    @SuppressWarnings("unused")
    private static boolean isPrime(int x) {
        if (x < 2) return false;
        for (int d = 2; d * d <= x; ++d) {
            if (x % d == 0) return false;
        }

        return true;
    }

    @SuppressWarnings("unused")
    private static int[] getPrimes(int n) {
        boolean[] used = new boolean[n];
        used[0] = used[1] = true;

        int size = 0;
        for (int i = 2; i < n; ++i) {
            if (!used[i]) {
                ++size;
                for (int j = 2 * i; j < n; j += i) {
                    used[j] = true;
                }
            }
        }

        int[] primes = new int[size];
        for (int i = 0, cur = 0; i < n; ++i) {
            if (!used[i]) {
                primes[cur++] = i;
            }
        }

        return primes;
    }

    /////////////////////////////////////////////////////////////////////

    @SuppressWarnings("unused")
    int[] getDivisors(int value) {
        List<Integer> divisors = new ArrayList<>();
        for (int divisor = 1; divisor * divisor <= value; ++divisor) {
            if (value % divisor == 0) {
                divisors.add(divisor);
                if (divisor * divisor != value) {
                    divisors.add(value / divisor);
                }
            }
        }

        return castInt(divisors);
    }

    @SuppressWarnings("unused")
    long[] getDivisors(long value) {
        List<Long> divisors = new ArrayList<>();
        for (long divisor = 1; divisor * divisor <= value; ++divisor) {
            if (value % divisor == 0) {
                divisors.add(divisor);
                if (divisor * divisor != value) {
                    divisors.add(value / divisor);
                }
            }
        }

        return castLong(divisors);
    }

    /////////////////////////////////////////////////////////////////////

    @SuppressWarnings("unused")
    private static long lcm(long a, long b) {
        return a / gcd(a, b) * b;
    }

    private static long gcd(long a, long b) {
        return (a == 0 ? b : gcd(b % a, a));
    }

    /////////////////////////////////////////////////////////////////////

    private static int[] castInt(List<Integer> list) {
        int[] array = new int[list.size()];
        for (int i = 0; i < array.length; ++i) {
            array[i] = list.get(i);
        }

        return array;
    }

    @SuppressWarnings("unused")
    private static long[] castLong(List<Long> list) {
        long[] array = new long[list.size()];
        for (int i = 0; i < array.length; ++i) {
            array[i] = list.get(i);
        }

        return array;
    }

    /////////////////////////////////////////////////////////////////////

    /**
     * Generates list with keys 0..<n
     * @param n - exclusive limit of sequence
     */
    @SuppressWarnings("unused")
    private static List<Integer> order(int n) {
        List<Integer> sequence = new ArrayList<>();
        for (int i = 0; i < n; ++i) {
            sequence.add(i);
        }

        return sequence;
    }
}