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.io.*;
import java.util.*;

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

public class Main {
    private static FastScanner in = new FastScanner();
    private static FastOutput out = new FastOutput();

    public void run() {
        int n = in.nextInt(), m = in.nextInt();
        
        long[] ns = new long[n], ms = new long[m];

        for (int i = 0; i < n; i++) {
            ns[i] = in.nextLong();
        }
        for (int i = 0; i < m; i++) {
            ms[i] = in.nextLong();
        }

        long ns_s = 0, ms_s = 0;
        for (int i = 0; i < n - 1; i++) {
            ns_s = ns_s ^ ns[i];
        }
        for (int i = 0; i < m - 1; i++) {
            ms_s = ms_s ^ ms[i];
        }

        String bits = Long.toBinaryString(ms_s);
        String need = Long.toBinaryString(ns[ns.length - 1]);

        int bitl = bits.length(), needl = need.length();
        int maxl = max(bitl, needl), minl = min(bitl, needl);
        char[] res = new char[maxl];

        for (int i = 0; i < maxl; i++) {
            if (i < minl) {
                if (bits.charAt(bitl - 1 - i) != need.charAt(needl - 1 - i)) {
                    res[maxl - 1 - i] = '1';
                } else {
                    res[maxl - 1 - i] = '0';
                }
            } else {
                if (bitl == minl)
                    res[maxl - 1 - i] = need.charAt(needl - 1 - i);
                else
                    res[maxl - 1 - i] = bits.charAt(bitl - 1 - i);
            }
        }

        String res_s = new String(res);
        long res_l = Long.parseLong(res_s, 2);

        if ((res_l ^ ns_s) != ms[ms.length - 1]) {
            out.println("NO");
            return;
        }
        out.println("YES");

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (i == n - 1 && j == m - 1) {
                    out.print(res_l);
                    continue;
                }
                if (i == n - 1) {
                    out.print(ms[j]);
                } else if (j == m - 1) {
                    out.print(ns[i]);
                } else {
                    out.print(0);
                }
            }
            out.println("");
        }
    }


    public static void main(String[] args) {
        new Main().run();
        out.flush();
        out.close();
    }
}

class FastScanner {
    BufferedReader br;
    StringTokenizer st;

    FastScanner() {
        this(System.in);
    }

    FastScanner(InputStream stream) {
        br = new BufferedReader(new InputStreamReader(stream));
    }

    FastScanner(File file) {
        try {
            br = new BufferedReader(new FileReader(file));
        } catch (FileNotFoundException e) {
            throw new RuntimeException(e);
        }
    }

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

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

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

class FastOutput {
    private final BufferedWriter bf;


    public FastOutput(OutputStream outputStream) {
        bf = new BufferedWriter(new OutputStreamWriter(outputStream));
    }

    public FastOutput() {
        this(System.out);
    }

    private void printOne(Object s) {
        try {
            bf.write(s.toString());
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    public void println(Object s) {
        printOne(s);
        printOne("\n");
    }

    public void print(Object ...os) {
        printd(" ", os);
    }

    public void printd(String delimiter, Object ...os) {
        for (Object o : os) {
            printOne(o);
            printOne(delimiter);
        }
    }

    public void flush() {
        try {
            bf.flush();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    public void close() {
        try {
            bf.close();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }
}