'''simple docstring'''






def  UpperCamelCase__					(					_lowercase    :				int = 1_0     )							->	Dict:
  if not isinstance(UpperCamelCase__   ,    UpperCamelCase__     ) or n < 0:
    raise ValueError("""Invalid input"""     )
  __UpperCAmelCase:					List[Any]		= 1_0**n
  __UpperCAmelCase:					List[str]		= 2_8_4_3_3 * (pow(2   ,    7_8_3_0_4_5_7   ,    UpperCamelCase__     )) + 1
  return str(number % modulus     )


if __name__ == "__main__":
    from doctest import testmod

    testmod()
    print(F"""{solution(10) = }""")





'''simple docstring'''






import inspect

import jax
import jax.lax as lax
import jax.numpy as jnp

from ..utils import add_start_docstrings
from ..utils.logging import get_logger


SCREAMING_SNAKE_CASE_	   =			get_logger(__name__)


SCREAMING_SNAKE_CASE_	   =			R'\n    Args:\n        input_ids (`jnp.ndarray` of shape `(batch_size, sequence_length)`):\n            Indices of input sequence tokens in the vocabulary.\n\n            Indices can be obtained using [`PreTrainedTokenizer`]. See [`PreTrainedTokenizer.encode`] and\n            [`PreTrainedTokenizer.__call__`] for details.\n\n            [What are input IDs?](../glossary#input-ids)\n        scores (`jnp.ndarray` of shape `(batch_size, config.vocab_size)`):\n            Prediction scores of a language modeling head. These can be logits for each vocabulary when not using beam\n            search or log softmax for each vocabulary token when using beam search\n        kwargs (`Dict[str, Any]`, *optional*):\n            Additional logits processor specific kwargs.\n\n    Return:\n        `jnp.ndarray` of shape `(batch_size, config.vocab_size)`: The processed prediction scores.\n\n'




class    a :



  """simple docstring"""







  @add_start_docstrings(snake_case_					)
  def __call__(							self   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    raise NotImplementedError(
        F'''{self.__class__} is an abstract class. Only classes inheriting this class can be called.'''					)




class    a :



  """simple docstring"""







  @add_start_docstrings(snake_case_					)
  def __call__(							self   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    raise NotImplementedError(
        F'''{self.__class__} is an abstract class. Only classes inheriting this class can be called.'''					)




class    a (       __lowerCAmelCase				):



  """simple docstring"""







  @add_start_docstrings(snake_case_					)
  def __call__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_   ,    **snake_case_					):

    '''simple docstring'''







    for processor in self:
      __UpperCAmelCase:					str		= inspect.signature(processor.__call__					).parameters
      if len(snake_case_					) > 3:
        if not all(arg in kwargs for arg in list(function_args.keys()					)[2:]					):
          raise ValueError(
              F'''Make sure that all the required parameters: {list(function_args.keys()					)} for '''
              F'''{processor.__class__} are passed to the logits processor.'''					)
        __UpperCAmelCase:					List[Any]		= processor(snake_case_   ,    snake_case_   ,    snake_case_   ,    **snake_case_					)
      else:
        __UpperCAmelCase:					Optional[Any]		= processor(snake_case_   ,    snake_case_   ,    snake_case_					)
    return scores




class    a (       __lowerCAmelCase				):



  """simple docstring"""







  def __init__(							self   ,    snake_case_					):

    '''simple docstring'''







    if not isinstance(snake_case_   ,    snake_case_					) or not (temperature > 0):
      raise ValueError(F'''`temperature` has to be a strictly positive float, but is {temperature}'''					)

    __UpperCAmelCase:					Any		= temperature







  def __call__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					Tuple		= scores / self.temperature
    return scores




class    a (       __lowerCAmelCase				):



  """simple docstring"""







  def __init__(							self   ,    snake_case_   ,    snake_case_ = -float("""Inf"""					)   ,    snake_case_ = 1					):

    '''simple docstring'''







    if not isinstance(snake_case_   ,    snake_case_					) or (top_p < 0 or top_p > 1.0):
      raise ValueError(F'''`top_p` has to be a float > 0 and < 1, but is {top_p}'''					)
    if not isinstance(snake_case_   ,    snake_case_					) or (min_tokens_to_keep < 1):
      raise ValueError(F'''`min_tokens_to_keep` has to be a positive integer, but is {min_tokens_to_keep}'''					)

    __UpperCAmelCase:					int		= top_p
    __UpperCAmelCase:					str		= filter_value
    __UpperCAmelCase:					List[Any]		= min_tokens_to_keep







  def __call__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase, __UpperCAmelCase:					List[Any]		= lax.top_k(snake_case_   ,    scores.shape[-1]					)

    __UpperCAmelCase:					Tuple		= jnp.full_like(snake_case_   ,    self.filter_value					)
    __UpperCAmelCase:					Optional[int]		= jax.nn.softmax(snake_case_   ,    axis=-1					).cumsum(axis=-1					)
    __UpperCAmelCase:					List[str]		= cumulative_probs < self.top_p

    # include the token that is higher than top_p as well
    __UpperCAmelCase:					str		= jnp.roll(snake_case_   ,    1					)
    score_mask |= score_mask.at[:, 0].set(snake_case_					)

    # min tokens to keep
    __UpperCAmelCase:					str		= score_mask.at[:, : self.min_tokens_to_keep].set(snake_case_					)

    __UpperCAmelCase:					List[Any]		= jnp.where(snake_case_   ,    snake_case_   ,    snake_case_					)
    __UpperCAmelCase:					Optional[Any]		= jax.lax.sort_key_val(snake_case_   ,    snake_case_					)[-1]

    return next_scores




class    a (       __lowerCAmelCase				):



  """simple docstring"""







  def __init__(							self   ,    snake_case_   ,    snake_case_ = -float("""Inf"""					)   ,    snake_case_ = 1					):

    '''simple docstring'''







    if not isinstance(snake_case_   ,    snake_case_					) or top_k <= 0:
      raise ValueError(F'''`top_k` has to be a strictly positive integer, but is {top_k}'''					)

    __UpperCAmelCase:					Optional[Any]		= max(snake_case_   ,    snake_case_					)
    __UpperCAmelCase:					List[str]		= filter_value







  def __call__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase, __UpperCAmelCase:					List[Any]		= scores.shape
    __UpperCAmelCase:					List[Any]		= jnp.full(batch_size * vocab_size   ,    self.filter_value					)

    __UpperCAmelCase:					Any		= min(self.top_k   ,    scores.shape[-1]					)  # Safety check
    __UpperCAmelCase, __UpperCAmelCase:					List[Any]		= lax.top_k(snake_case_   ,    snake_case_					)
    __UpperCAmelCase:					Optional[Any]		= jnp.broadcast_to((jnp.arange(snake_case_					) * vocab_size)[:, None]   ,    (batch_size, topk)					).flatten()
    __UpperCAmelCase:					List[Any]		= topk_scores.flatten()
    __UpperCAmelCase:					str		= topk_indices.flatten() + shift

    __UpperCAmelCase:					List[Any]		= next_scores_flat.at[topk_indices_flat].set(snake_case_					)
    __UpperCAmelCase:					Any		= next_scores_flat.reshape(snake_case_   ,    snake_case_					)
    return next_scores




class    a (       __lowerCAmelCase				):



  """simple docstring"""







  def __init__(							self   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					List[Any]		= bos_token_id







  def __call__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					List[Any]		= jnp.full(scores.shape   ,    -float("""inf"""					)					)

    __UpperCAmelCase:					Optional[Any]		= 1 - jnp.bool_(cur_len - 1					)

    __UpperCAmelCase:					Any		= jnp.where(snake_case_   ,    new_scores.at[:, self.bos_token_id].set(0					)   ,    snake_case_					)

    return scores




class    a (       __lowerCAmelCase				):



  """simple docstring"""







  def __init__(							self   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					Union[str, Any]		= max_length
    __UpperCAmelCase:					List[str]		= eos_token_id







  def __call__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					Optional[int]		= jnp.full(scores.shape   ,    -float("""inf"""					)					)

    __UpperCAmelCase:					List[str]		= 1 - jnp.bool_(cur_len - self.max_length + 1					)

    __UpperCAmelCase:					Any		= jnp.where(snake_case_   ,    new_scores.at[:, self.eos_token_id].set(0					)   ,    snake_case_					)

    return scores




class    a (       __lowerCAmelCase				):



  """simple docstring"""







  def __init__(							self   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    if not isinstance(snake_case_   ,    snake_case_					) or min_length < 0:
      raise ValueError(F'''`min_length` has to be a positive integer, but is {min_length}'''					)

    if not isinstance(snake_case_   ,    snake_case_					) or eos_token_id < 0:
      raise ValueError(F'''`eos_token_id` has to be a positive integer, but is {eos_token_id}'''					)

    __UpperCAmelCase:					List[Any]		= min_length
    __UpperCAmelCase:					Optional[int]		= eos_token_id







  def __call__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					Union[str, Any]		= 1 - jnp.clip(cur_len - self.min_length   ,    0   ,    1					)

    __UpperCAmelCase:					int		= jnp.where(snake_case_   ,    scores.at[:, self.eos_token_id].set(-float("""inf"""					)					)   ,    snake_case_					)

    return scores




class    a (       __lowerCAmelCase				):



  """simple docstring"""







  def __init__(							self   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					Any		= list(snake_case_					)
    __UpperCAmelCase:					Optional[Any]		= begin_index







  def __call__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					Union[str, Any]		= 1 - jnp.bool_(cur_len - self.begin_index					)

    __UpperCAmelCase:					str		= jnp.where(snake_case_   ,    scores.at[:, self.begin_suppress_tokens].set(-float("""inf"""					)					)   ,    snake_case_					)

    return scores




class    a (       __lowerCAmelCase				):



  """simple docstring"""







  def __init__(							self   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					Optional[Any]		= list(snake_case_					)







  def __call__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					int		= scores.at[..., self.suppress_tokens].set(-float("""inf"""					)					)

    return scores




class    a (       __lowerCAmelCase				):



  """simple docstring"""







  def __init__(							self   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					Optional[int]		= dict(snake_case_					)
    # Converts the dictionary of format {index: token} containing the tokens to be forced to an array, where the
    # index of the array corresponds to the index of the token to be forced, for XLA compatibility.
    # Indexes without forced tokens will have a negative value.
    __UpperCAmelCase:					Optional[Any]		= jnp.ones((max(force_token_map.keys()					) + 1)   ,    dtype=jnp.intaa					) * -1
    for index, token in force_token_map.items():
      if token is not None:
        __UpperCAmelCase:					Union[str, Any]		= force_token_array.at[index].set(snake_case_					)
    __UpperCAmelCase:					Union[str, Any]		= jnp.intaa(snake_case_					)







  def __call__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    def _force_token(snake_case_					):
      __UpperCAmelCase:					List[Any]		= scores.shape[0]
      __UpperCAmelCase:					int		= self.force_token_array[generation_idx]

      __UpperCAmelCase:					Union[str, Any]		= jnp.ones_like(snake_case_   ,    dtype=scores.dtype					) * -float("""inf"""					)
      __UpperCAmelCase:					List[Any]		= jnp.zeros((batch_size, 1)   ,    dtype=scores.dtype					)
      __UpperCAmelCase:					List[Any]		= lax.dynamic_update_slice(snake_case_   ,    snake_case_   ,    (0, current_token)					)
      return new_scores

    __UpperCAmelCase:					Optional[int]		= lax.cond(
        cur_len >= self.force_token_array.shape[0]   ,    lambda: scores   ,    lambda: lax.cond(
            self.force_token_array[cur_len] >= 0   ,    lambda: _force_token(snake_case_					)   ,    lambda: scores   ,    )   ,    )
    return scores




class    a (       __lowerCAmelCase				):



  """simple docstring"""







  def __init__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					int		= generate_config.eos_token_id
    __UpperCAmelCase:					Union[str, Any]		= generate_config.no_timestamps_token_id
    __UpperCAmelCase:					Tuple		= generate_config.no_timestamps_token_id + 1

    __UpperCAmelCase:					Any		= decoder_input_length + 1

    if generate_config.is_multilingual:
      # room for language token and task token
      self.begin_index += 2
    if hasattr(snake_case_   ,    """max_initial_timestamp_index"""					):
      __UpperCAmelCase:					Optional[int]		= generate_config.max_initial_timestamp_index
    else:
      __UpperCAmelCase:					List[str]		= model_config.vocab_size
    if self.max_initial_timestamp_index is None:
      __UpperCAmelCase:					Any		= model_config.vocab_size







  def __call__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					Any		= scores.at[:, self.no_timestamps_token_id].set(-float("""inf"""					)					)

    def handle_pairs(snake_case_   ,    snake_case_					):
      __UpperCAmelCase:					Optional[int]		= jnp.where((cur_len - self.begin_index) >= 1   ,    snake_case_   ,    snake_case_					)
      __UpperCAmelCase:					Union[str, Any]		= jnp.where(
          input_ids_k[cur_len - 1] >= self.timestamp_begin   ,    True and last_was_timestamp   ,    snake_case_   ,    )

      __UpperCAmelCase:					Union[str, Any]		= jnp.where((cur_len - self.begin_index) < 2   ,    snake_case_   ,    snake_case_					)
      __UpperCAmelCase:					List[str]		= jnp.where(
          input_ids_k[cur_len - 2] >= self.timestamp_begin   ,    snake_case_   ,    snake_case_   ,    )

      return jnp.where(
          snake_case_   ,    jnp.where(
              penultimate_was_timestamp > 0   ,    scores_k.at[self.timestamp_begin :].set(-float("""inf"""					)					)   ,    scores_k.at[: self.eos_token_id].set(-float("""inf"""					)					)   ,    )   ,    snake_case_   ,    )

    __UpperCAmelCase:					Dict		= jax.vmap(snake_case_					)(snake_case_   ,    snake_case_					)

    __UpperCAmelCase:					Dict		= jnp.where(cur_len == self.begin_index   ,    snake_case_   ,    snake_case_					)
    __UpperCAmelCase:					List[Any]		= jnp.where(
        self.max_initial_timestamp_index is not None   ,    True and apply_max_initial_timestamp   ,    snake_case_   ,    )

    __UpperCAmelCase:					List[str]		= self.timestamp_begin + self.max_initial_timestamp_index

    __UpperCAmelCase:					List[str]		= jnp.where(
        snake_case_   ,    scores.at[:, last_allowed + 1 :].set(-float("""inf"""					)					)   ,    snake_case_   ,    )

    # if sum of probability over timestamps is above any other token, sample timestamp
    __UpperCAmelCase:					Union[str, Any]		= jax.nn.log_softmax(snake_case_   ,    axis=-1					)

    def handle_cumulative_probs(snake_case_   ,    snake_case_					):
      __UpperCAmelCase:					int		= jax.nn.logsumexp(logprobs_k[self.timestamp_begin :]   ,    axis=-1					)
      __UpperCAmelCase:					Tuple		= jnp.max(logprobs_k[: self.timestamp_begin]					)
      return jnp.where(
          timestamp_logprob > max_text_token_logprob   ,    scores_k.at[: self.timestamp_begin].set(-float("""inf"""					)					)   ,    snake_case_   ,    )

    __UpperCAmelCase:					Tuple		= jax.vmap(snake_case_					)(snake_case_   ,    snake_case_					)

    return scores