import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.stream.IntStream;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.security.AccessControlException;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.util.regex.Pattern;
import java.io.InputStream;

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

    static class DDoubleLandscape {
        private static final int MOD = (int) 1e9 + 7;

        public void solve(int testNumber, LightScanner in, LightWriter out) {
            Debug.autoEnable();
            int n = in.ints();
            int m = in.ints();
            int[] a = in.ints(n);
            int[] b = in.ints(m);
            int[] rowhint = new int[n * m + 1];
            int[] columnhint = new int[n * m + 1];
            Arrays.fill(rowhint, -1);
            Arrays.fill(columnhint, -1);
            for (int i = 0; i < n; i++) {
                if (columnhint[a[i]] >= 0) {
                    out.ans(0).ln();
                    return;
                }
                columnhint[a[i]] = i;
            }
            for (int i = 0; i < m; i++) {
                if (rowhint[b[i]] >= 0) {
                    out.ans(0).ln();
                    return;
                }
                rowhint[b[i]] = i;
            }

            long ans = 1;
            int rf = 0, cf = 0;
            for (int k = n * m; k > 0; k--) {
                if (rowhint[k] >= 0 && columnhint[k] >= 0) {
                    rf++;
                    cf++;
                } else if (rowhint[k] >= 0) {
                    ans *= cf;
                    ans %= MOD;
                    rf++;
                } else if (columnhint[k] >= 0) {
                    ans *= rf;
                    ans %= MOD;
                    cf++;
                } else {
                    ans *= (cf * rf) - (n * m - k);
                    ans %= MOD;
                }
            }
            out.ans(ans).ln();
        }

    }

    static class Debug {
        private static final String DEBUG_PROPERTY = "enabled";
        private static final String DEBUG_CALL_PATTERN = "^.+\\.debug\\(([a-zA-Z0-9]+)\\);.*$";
        private static Pattern debugRegex;
        private static boolean enabled = false;
        private static String src;

        public static void autoEnable() {
            try {
                src = System.getProperty(DEBUG_PROPERTY);
                if (src != null) {
                    enabled = true;
                    if (debugRegex == null) {
                        debugRegex = Pattern.compile(DEBUG_CALL_PATTERN);
                    }
                }
            } catch (AccessControlException ex) {
                src = null;
            }
        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new BufferedWriter(new OutputStreamWriter(out, Charset.defaultCharset())));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(long l) {
            return ans(Long.toString(l));
        }

        public LightWriter ans(int i) {
            return ans(Integer.toString(i));
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

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

        public int ints() {
            return Integer.parseInt(string());
        }

        public int[] ints(int length) {
            return IntStream.range(0, length).map(x -> ints()).toArray();
        }

    }
}



Measured memory_bytes: 36820