
from __future__ import annotations







def 							UpperCAmelCase_(  a__      ,		a__ = None					):



    """simple docstring"""



    SCREAMING_SNAKE_CASE							:							Dict								=      word_bank or []
    # create a table
    SCREAMING_SNAKE_CASE							:							int								=      len(_A					) + 1

    SCREAMING_SNAKE_CASE							:							Optional[int]								=      []
    for _ in range(_A					):
        table.append([]					)
    # seed value
    SCREAMING_SNAKE_CASE							:							List[Any]								=      [[]]  # because empty string has empty combination

    # iterate through the indices
    for i in range(_A					):
        # condition
        if table[i] != []:
            for word in word_bank:
                # slice condition
                if target[i : i + len(_A					)] == word:
                    SCREAMING_SNAKE_CASE							:							Union[str, Any]								=      [
                        [word, *way] for way in table[i]
                    ]
                    # adds the word to every combination the current position holds
                    # now,push that combination to the table[i+len(word)]
                    table[i + len(_A					)] += new_combinations

    # combinations are in reverse order so reverse for better output
    for combination in table[len(_A					)]:
        combination.reverse()

    return table[len(_A					)]


if __name__ == "__main__":
      print(all_construct('''jwajalapa''', ['''jwa''', '''j''', '''w''', '''a''', '''la''', '''lapa''']))
      print(all_construct('''rajamati''', ['''s''', '''raj''', '''amat''', '''raja''', '''ma''', '''i''', '''t''']))
      print(
          all_construct(
              '''hexagonosaurus''',
              ['''h''', '''ex''', '''hex''', '''ag''', '''ago''', '''ru''', '''auru''', '''rus''', '''go''', '''no''', '''o''', '''s'''],
          )
      )

'''simple docstring'''




def 				snake_case__							(			_A:					int      ,   _A:					int )    ->	int:

		'''simple docstring'''


		while a != 0:
				lowerCAmelCase					,     lowerCAmelCase   					=  b % a, a
		return b






def 				snake_case__							(			_A:					int      ,   _A:					int )    ->	int:

		'''simple docstring'''


		if gcd(_A      ,   _A ) != 1:
				lowerCAmelCase   					=  f"mod inverse of {a!r} and {m!r} does not exist"
				raise ValueError(_A )
		lowerCAmelCase					,     lowerCAmelCase					,     lowerCAmelCase   					=  1, 0, a
		lowerCAmelCase					,     lowerCAmelCase					,     lowerCAmelCase   					=  0, 1, m
		while va != 0:
				lowerCAmelCase   					=  ua // va
				lowerCAmelCase					,     lowerCAmelCase					,     lowerCAmelCase					,     lowerCAmelCase					,     lowerCAmelCase					,     lowerCAmelCase   					=  (ua - q * va), (ua - q * va), (ua - q * va), va, va, va
		return ua % m




