import java.util.Arrays;

public class Main {

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

    int mod = (int) 1e9 + 7;

    Arrays.sort(a);
    Arrays.sort(b);

    boolean[] used = new boolean[n * m + 1];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        if (a[i] == b[j]) {
          if (used[a[i]]) {
            System.out.println(0);
            return;
          }
          used[a[i]] = true;
        }
      }
    }

    long ret = 1;

    int cnt = 0;
    for (int i = n * m; i >= 1; i--) {
      int p = lowerBound(a, i);
      int q = lowerBound(b, i);

      if (n == p || m == q) {
        System.out.println(0);
        return;
      }
      if (a[p] == i && b[q] == i) {
      } else if (a[p] == i) {
        ret *= m - q;
      } else if (b[q] == i) {
        ret *= n - p;
      } else {
        ret *= Math.max(0, (n - p) * (m - q) - cnt);
      }
      cnt++;
      ret %= mod;
    }

    System.out.println(ret);
  }

  public static int lowerBound(int[] a, int v) {
    int low = -1, high = a.length;
    while (high - low > 1) {
      int h = high + low >>> 1;
      if (a[h] >= v) {
        high = h;
      } else {
        low = h;
      }
    }
    return high;
  }

  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: 38004