




'''simple docstring'''







from __future__ import annotations

from collections.abc import MutableSequence


class     _a						:
       def __init__(			self		:			Union[str, Any]     ,       lowercase		:			int     ,       lowercase		:			MutableSequence[float]       ):



           '''simple docstring'''

           if len(lowercase       ) != degree + 1:
               raise ValueError(
                   '''The number of coefficients should be equal to the degree + 1.'''       )

           UpperCAmelCase     =	list(lowercase       )
           UpperCAmelCase     =	degree
       def __add__(			self		:			str     ,       lowercase		:			Polynomial       ):



           '''simple docstring'''

           if self.degree > polynomial_a.degree:
               UpperCAmelCase     =	self.coefficients[:]
               for i in range(polynomial_a.degree + 1       ):
                   coefficients[i] += polynomial_a.coefficients[i]
               return Polynomial(self.degree     ,       lowercase       )
           else:
               UpperCAmelCase     =	polynomial_a.coefficients[:]
               for i in range(self.degree + 1       ):
                   coefficients[i] += self.coefficients[i]
               return Polynomial(polynomial_a.degree     ,       lowercase       )
       def __sub__(			self		:			int     ,       lowercase		:			Polynomial       ):



           '''simple docstring'''

           return self + polynomial_a * Polynomial(0     ,       [-1]       )
       def __neg__(			self		:			Tuple       ):



           '''simple docstring'''

           return Polynomial(self.degree     ,       [-c for c in self.coefficients]       )
       def __mul__(			self		:			Optional[int]     ,       lowercase		:			Polynomial       ):



           '''simple docstring'''

           UpperCAmelCase     =	[0] * (self.degree + polynomial_a.degree + 1)
           for i in range(self.degree + 1       ):
               for j in range(polynomial_a.degree + 1       ):
                   coefficients[i + j] += (
                       self.coefficients[i] * polynomial_a.coefficients[j]
                   )

           return Polynomial(self.degree + polynomial_a.degree     ,       lowercase       )
       def 					A   (			self		:			str     ,       lowercase		:			int | float       ):



           '''simple docstring'''

           UpperCAmelCase     =	0
           for i in range(self.degree + 1       ):
               result += self.coefficients[i] * (substitution**i)
           return result
       def __str__(			self		:			List[str]       ):



           '''simple docstring'''

           UpperCAmelCase     =	''''''
           for i in range(self.degree     ,       -1     ,       -1       ):
               if self.coefficients[i] == 0:
                   continue
               elif self.coefficients[i] > 0:
                   if polynomial:
                       polynomial += " + "
               else:
                   polynomial += " - "

               if i == 0:
                   polynomial += str(abs(self.coefficients[i]       )       )
               elif i == 1:
                   polynomial += str(abs(self.coefficients[i]       )       ) + "x"
               else:
                   polynomial += str(abs(self.coefficients[i]       )       ) + "x^" + str(lowercase       )

           return polynomial
       def __repr__(			self		:			List[Any]       ):



           '''simple docstring'''

           return self.__str__()
       def 					A   (			self		:			Dict       ):



           '''simple docstring'''

           UpperCAmelCase     =	[0] * self.degree
           for i in range(self.degree       ):
               UpperCAmelCase     =	self.coefficients[i + 1] * (i + 1)
           return Polynomial(self.degree - 1     ,       lowercase       )
       def 					A   (			self		:			Dict     ,       lowercase		:			int | float = 0       ):



           '''simple docstring'''

           UpperCAmelCase     =	[0] * (self.degree + 2)
           UpperCAmelCase     =	constant
           for i in range(self.degree + 1       ):
               UpperCAmelCase     =	self.coefficients[i] / (i + 1)
           return Polynomial(self.degree + 1     ,       lowercase       )
       def __eq__(			self		:			Dict     ,       lowercase		:			object       ):



           '''simple docstring'''

           if not isinstance(lowercase     ,       lowercase       ):
               return False

           if self.degree != polynomial_a.degree:
               return False

           for i in range(self.degree + 1       ):
               if self.coefficients[i] != polynomial_a.coefficients[i]:
                   return False

           return True







       def __ne__(			self		:			Optional[Any]     ,       lowercase		:			object       ):



           '''simple docstring'''

           return not self.__eq__(lowercase       )










'''simple docstring'''







from __future__ import annotations





def 		snake_case_							(_a			:							str					,     _a			:							list[str] | None = None  ):
    UpperCAmelCase     =	word_bank or []
    # create a table
    UpperCAmelCase     =	len(_a  ) + 1

    UpperCAmelCase     =	[]
    for _ in range(_a  ):
        table.append([]  )
    # seed value
    UpperCAmelCase     =	[[]]  # 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:
                    UpperCAmelCase     =	[
                        [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'],
       )
   )




