

def 						lowerCamelCase__      ( __A    :int	,__A    :list[int]	,__A    :int		):


       """simple docstring"""




       def count_of_possible_combinations(__A    :int		) -> int:
              if target < 0:
                     return 0
              if target == 0:
                     return 1
              return sum(count_of_possible_combinations(target - item		) for item in array		)

       return count_of_possible_combinations(__A		)







def 						lowerCamelCase__      ( __A    :int	,__A    :list[int]	,__A    :int		):


       """simple docstring"""




       def count_of_possible_combinations_with_dp_array(
           __A    :int	,__A    :list[int]		) -> int:
              if target < 0:
                     return 0
              if target == 0:
                     return 1
              if dp_array[target] != -1:
                     return dp_array[target]
              __snake_case       	=							sum(
                  count_of_possible_combinations_with_dp_array(target - item	,__A		)
                  for item in array		)
              __snake_case       	=							answer
              return answer

       __snake_case       	=							[-1] * (target + 1)
       return count_of_possible_combinations_with_dp_array(__A	,__A		)







def 						lowerCamelCase__      ( __A    :int	,__A    :list[int]	,__A    :int		):


       """simple docstring"""




       __snake_case       	=							[0] * (target + 1)
       __snake_case       	=							1

       for i in range(1	,target + 1		):
              for j in range(__A		):
                     if i - array[j] >= 0:
                            dp_array[i] += dp_array[i - array[j]]

       return dp_array[target]


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    UpperCamelCase__		 =     3
    UpperCamelCase__		 =     5
    UpperCamelCase__		 =     [1, 2, 5]
    print(combination_sum_iv(n, array, target))




def 						lowerCamelCase__      ( __A    :int	,__A    :int		):


       """simple docstring"""




       if a < 0 or b < 0:
              raise ValueError("""the value of both inputs must be positive"""		)

       __snake_case       	=							str(bin(__A		)		)[2:]  # remove the leading "0b"
       __snake_case       	=							str(bin(__A		)		)[2:]  # remove the leading "0b"

       __snake_case       	=							max(len(__A		)	,len(__A		)		)

       return "0b" + "".join(
           str(int(char_a == """1""" and char_b == """1"""		)		)
           for char_a, char_b in zip(a_binary.zfill(__A		)	,b_binary.zfill(__A		)		)		)


if __name__ == "__main__":
    import doctest

    doctest.testmod()

