

from __future__ import annotations

import math
import random







def       snake_case__    (       lowerCAmelCase_,   lowerCAmelCase_,   lowerCAmelCase_      ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE										=d * e - 1
     SCREAMING_SNAKE_CASE										=0
     SCREAMING_SNAKE_CASE										=0
     while p == 0:
          SCREAMING_SNAKE_CASE										=random.randint(2,   n - 1      )
          SCREAMING_SNAKE_CASE										=k
          while True:
               if t % 2 == 0:
                    SCREAMING_SNAKE_CASE										=t // 2
                    SCREAMING_SNAKE_CASE										=(g**t) % n
                    SCREAMING_SNAKE_CASE										=math.gcd(x - 1,   lowerCAmelCase_      )
                    if x > 1 and y > 1:
                         SCREAMING_SNAKE_CASE										=y
                         SCREAMING_SNAKE_CASE										=n // y
                         break  # find the correct factors
               else:
                    break  # t is not divisible by 2, break and choose another g
     return sorted([p, q]      )


if __name__ == "__main__":
 import doctest

 doctest.testmod()




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_torch_available


_lowerCamelCase								={
    "configuration_xlm_prophetnet": ["XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP", "XLMProphetNetConfig"],
}

try:
 if not is_sentencepiece_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCamelCase								=["XLMProphetNetTokenizer"]

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCamelCase								=[
     "XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST",
     "XLMProphetNetDecoder",
     "XLMProphetNetEncoder",
     "XLMProphetNetForCausalLM",
     "XLMProphetNetForConditionalGeneration",
     "XLMProphetNetModel",
     "XLMProphetNetPreTrainedModel",
 ]


if TYPE_CHECKING:
 from .configuration_xlm_prophetnet import XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP, XLMProphetNetConfig

 try:
  if not is_sentencepiece_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_xlm_prophetnet import XLMProphetNetTokenizer

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_xlm_prophetnet import (
      XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST,
      XLMProphetNetDecoder,
      XLMProphetNetEncoder,
      XLMProphetNetForCausalLM,
      XLMProphetNetForConditionalGeneration,
      XLMProphetNetModel,
      XLMProphetNetPreTrainedModel,
  )

else:
 import sys

 _lowerCamelCase								=_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)

