public class Main {


  private static void solve() {
    int n = ni();
    int m = ni();
    int[] a = na(n);
    int[] b = na(m);
    

    int[] ac = new int[n * m + 1];
    int[] bc = new int[n * m + 1];
    boolean[] fixed = new boolean[n * m + 1];
    boolean[] ap = new boolean[m * n + 1];
    boolean[] bp = new boolean[m * n + 1];
    int[] cnt = new int[n * m + 1];
    for (int i = 0; i < n; i ++) {
      for (int j = 0; j < m; j ++) {
        if (a[i] <= b[j]) ac[a[i]] ++;
        if (b[j] <= a[i]) bc[b[j]] ++;
        if (a[i] == b[j]) {
          if (fixed[a[i]]) {
            System.out.println(0);
            return;
          }
          fixed[a[i]] = true;
        }
        ap[a[i]] = true;
        bp[b[j]] = true;
        cnt[Math.min(a[i], b[j])] ++;
      }
    }
    for (int i = n * m - 1; i > 0; i --) {
      cnt[i] += cnt[i + 1];
    }


    int mod = (int)1e9 + 7;
    long ret = 1;
    for (int i = n * m; i >= 1; i --) {
      if (fixed[i]) continue;
      if (ap[i]) {
        ret *= ac[i];
      } else if (bp[i]) {
        ret *= bc[i];
      } else {
        ret *= cnt[i] - (n * m - i);
      }
      ret %= mod;
    }
    System.out.println(ret);
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

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

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}


Measured memory_bytes: 46932