


import math







def     _lowercase							(  __lowerCamelCase      :       List[str]      )	-> list[int]:





     '''simple docstring'''





     UpperCamelCase__				:	Union[str, Any]										=  []
     UpperCamelCase__				:	str										=  2
     UpperCamelCase__				:	List[str]										=  int(math.sqrt(SCREAMING_SNAKE_CASE_      )      )  # Size of every segment
     UpperCamelCase__				:	Tuple										=  [True] * (end + 1)
     UpperCamelCase__				:	Dict										=  []

     while start <= end:
          if temp[start] is True:
               in_prime.append(SCREAMING_SNAKE_CASE_      )
               for i in range(start * start		,end + 1		,SCREAMING_SNAKE_CASE_      ):
                    UpperCamelCase__				:	Union[str, Any]										=  False
          start += 1
     prime += in_prime

     UpperCamelCase__				:	int										=  end + 1
     UpperCamelCase__				:	Dict										=  min(2 * end		,SCREAMING_SNAKE_CASE_      )

     while low <= n:
          UpperCamelCase__				:	List[str]										=  [True] * (high - low + 1)
          for each in in_prime:
               UpperCamelCase__				:	List[Any]										=  math.floor(low / each      ) * each
               if t < low:
                    t += each

               for j in range(SCREAMING_SNAKE_CASE_		,high + 1		,SCREAMING_SNAKE_CASE_      ):
                    UpperCamelCase__				:	Union[str, Any]										=  False

          for j in range(len(SCREAMING_SNAKE_CASE_      )      ):
               if temp[j] is True:
                    prime.append(j + low      )

          UpperCamelCase__				:	str										=  high + 1
          UpperCamelCase__				:	Dict										=  min(high + end		,SCREAMING_SNAKE_CASE_      )

     return prime







print(sieve(10**6))







def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			)->						str:



    """simple docstring"""






    if isinstance(SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			):
        raise TypeError("'float' object cannot be interpreted as an integer"			)
    if isinstance(SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			):
        raise TypeError("'str' object cannot be interpreted as an integer"			)

    if num == 0:
        return "0b0"

    UpperCamelCase_			  =						False

    if num < 0:
        UpperCamelCase_			  =						True
        UpperCamelCase_			  =						-num

    UpperCamelCase_			  =						[]
    while num > 0:
        binary.insert(0			,						num % 2			)
        num >>= 1

    if negative:
        return "-0b" + "".join(str(SCREAMING_SNAKE_CASE_			) for e in binary			)

    return "0b" + "".join(str(SCREAMING_SNAKE_CASE_			) for e in binary			)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
