long result = 1;
      for (int i = n1 + 1; i <= n2; i++) {
        result *= i;
      }
      return BigInteger.valueOf(result);
    }

    /*
     * We want each multiplication to have both sides with approximately the same number of digits.
     * Currently, we just divide the range in half.
     */
    int mid = (n1 + n2) >>> 1;

<img src="/img/tutorial/sub-applications/image02.png">

If you try interacting with any of the two user interfaces, they will work correctly, because the browser will be able to talk to each specific app or sub-app.

### Technical Details: `root_path`

var KafkaSHA512 scram.HashGeneratorFcn = sha512.New

// XDGSCRAMClient implements the client-side of an authentication
// conversation with a server.  A new conversation must be created for
// each authentication attempt.
type XDGSCRAMClient struct {
	*scram.Client
	*scram.ClientConversation
	scram.HashGeneratorFcn
}

// Begin constructs a SCRAM client component based on a given hash.Hash

   */
  Set<E> elementSet();

  /**
   * Returns a view of the contents of this multiset, grouped into {@code Multiset.Entry} instances,
   * each providing an element of the multiset and the count of that element. This set contains
   * exactly one entry for each distinct element in the multiset (thus it always has the same size
   * as the {@link #elementSet}). The order of the elements in the element set is unspecified.
   *

	Kubeconfig string
	Context    string
	Namespace  string
}

// Inherit the common kubernetes flags defined in the root package. This is a bit of a hack,
// but it allows us to directly get the final values for each of these flags without needing
// to pass pointers-to-flags through all of the (sub)commands.
func (o *KubeOptions) prepare(ctx cli.Context) {
	o.Namespace = ctx.Namespace()
	if o.Namespace == "" {

                excludedPackages.add(baseName);
            } else {
                excludedPackages.add(excludePattern);
            }
        }

        repository.each(new Action<ClassMetaData>() {
            @Override
            public void execute(ClassMetaData classMetaData) {
                if (classMetaData.getOuterClassName() != null) {
                    // Ignore inner classes

class BinaryCompatibilityRepositorySetupRule(private val params: Map<String, Any>) : SetupRule {

    companion object {
        const val REPOSITORY_CONTEXT_KEY = "binaryCompatibilityRepository"
    }

    /**
     * Each param is a `Set<String>`.
     */
    object Params {
        const val sourceRoots = "sourceRoots"
        const val sourceCompilationClasspath = "sourceCompilationClasspath"
    }

    @Suppress("unchecked_cast")

 * Dependency is the output of the <dfn>collection</dfn> process, which builds the graph of dependencies,
 * followed by <dfn>flattening</dfn> and <dfn>resolution</dfn>.
 * The version selection is done for each dependency during the collection phase.
 * The flatten phase will keep only a single version per ({@code groupId}, {@code artifactId}) pair.
 * The resolution will actually download the dependencies (or artifacts) that have been computed.

    MavenExecutionResult setDependencyResolutionResult(DependencyResolutionResult result);

    DependencyResolutionResult getDependencyResolutionResult();

    // for each exception
    // - knowing what artifacts are missing
    // - project building exception
    // - invalid project model exception: list of markers
    // - xmlpull parser exception
    List<Throwable> getExceptions();

namespace tensorflow {
namespace parallel_device {

// Allocate a parallel device named `device_name` which forwards operations to
// `underlying_devices`, maintaining "parallel tensors" with components placed
// on each underlying device.
//
// For example if `device_name` is
//   "/job:localhost/replica:0/task:0/device:CUSTOM:0"
// and `underlying_devices` is
//   {"/job:localhost/replica:0/task:0/device:GPU:0",