}

    BigInteger accum = BigInteger.ONE;

    long numeratorAccum = n;
    long denominatorAccum = 1;

    int bits = LongMath.log2(n, CEILING);

    int numeratorBits = bits;

    for (int i = 1; i < k; i++) {
      int p = n - i;
      int q = i + 1;

      // log2(p) >= bits - 1, because p >= n/2

      if (numeratorBits + bits >= Long.SIZE - 1) {

from fastapi import FastAPI

app = FastAPI()


@app.get("/items/{item_id}")
async def read_user_item(
    item_id: str, needy: str, skip: int = 0, limit: int | None = None
):
    item = {"item_id": item_id, "needy": needy, "skip": skip, "limit": limit}

      }
    }
  }

  private static class Sink extends AbstractStreamingHasher {
    final int chunkSize;
    final int bufferSize;
    final ByteArrayOutputStream out = new ByteArrayOutputStream();

    int processCalled = 0;
    boolean remainingCalled = false;

    Sink(int chunkSize, int bufferSize) {
      super(chunkSize, bufferSize);
      this.chunkSize = chunkSize;

class User(BaseModel):
    username: str
    full_name: Union[str, None] = None


@app.put("/items/{item_id}")
async def update_item(
    item_id: int, item: Item, user: User, importance: Annotated[int, Body()]
):
    results = {"item_id": item_id, "item": item, "user": user, "importance": importance}

      return forwardList;
    }

    private int reverseIndex(int index) {
      int size = size();
      checkElementIndex(index, size);
      return (size - 1) - index;
    }

    private int reversePosition(int index) {
      int size = size();
      checkPositionIndex(index, size);
      return size - index;
    }

    @Override
    public void add(int index, @ParametricNullness T element) {

        return this.binding.toString();
    }


    protected abstract void doSendFragment ( byte[] buf, int off, int length ) throws IOException;


    protected abstract int doReceiveFragment ( byte[] buf ) throws IOException;


    protected abstract int doSendReceiveFragment ( byte[] out, int off, int length, byte[] inB ) throws IOException;


    @Override
    public void close () throws IOException {

        int start = dstIndex;

        SMBUtil.writeInt2(41, dst, dstIndex);
        dst[ dstIndex + 2 ] = this.infoType;
        dst[ dstIndex + 3 ] = this.fileInfoClass;
        dstIndex += 4;

        SMBUtil.writeInt4(this.outputBufferLength, dst, dstIndex);
        dstIndex += 4;
        int inBufferOffsetOffset = dstIndex;
        dstIndex += 4;

class HeroBase(SQLModel):
    name: str = Field(index=True)
    age: Union[int, None] = Field(default=None, index=True)


class Hero(HeroBase, table=True):
    id: Union[int, None] = Field(default=None, primary_key=True)
    secret_name: str


class HeroPublic(HeroBase):
    id: int


class HeroCreate(HeroBase):
    secret_name: str


class HeroUpdate(HeroBase):

class HeroBase(SQLModel):
    name: str = Field(index=True)
    age: Union[int, None] = Field(default=None, index=True)


class Hero(HeroBase, table=True):
    id: Union[int, None] = Field(default=None, primary_key=True)
    secret_name: str


class HeroPublic(HeroBase):
    id: int


class HeroCreate(HeroBase):
    secret_name: str


class HeroUpdate(HeroBase):

  private final transient int mask;
  private final transient int hashCode;

  static <K, V> ImmutableBiMap<K, V> fromEntries(Entry<K, V>... entries) {
    return fromEntryArray(entries.length, entries);
  }

  static <K, V> ImmutableBiMap<K, V> fromEntryArray(int n, @Nullable Entry<K, V>[] entryArray) {
    checkPositionIndex(n, entryArray.length);
    int tableSize = Hashing.closedTableSize(n, MAX_LOAD_FACTOR);