
'''simple docstring'''






from __future__ import annotations

import math







def 		A_       (	_lowerCAmelCase   :    float				,	_lowerCAmelCase   :    int							):



      """simple docstring"""




      _lowerCamelCase				:   Optional[int]								=   u
      for i in range(1				,	lowerCamelCase_							):
            _lowerCamelCase				:   Optional[Any]								=   temp * (u - i)
      return temp







def 		A_       (	):



      """simple docstring"""




      _lowerCamelCase				:   Optional[int]								=   int(input("enter the numbers of values: "							)							)
      _lowerCamelCase				:   list[list[float]]								=   []
      for _ in range(lowerCamelCase_							):
            y.append([]							)
      for i in range(lowerCamelCase_							):
            for j in range(lowerCamelCase_							):
                  y[i].append(lowerCamelCase_							)
                  _lowerCamelCase				:   int								=   0

      print("enter the values of parameters in a list: "							)
      _lowerCamelCase				:   Optional[int]								=   list(map(lowerCamelCase_				,	input().split()							)							)

      print("enter the values of corresponding parameters: "							)
      for i in range(lowerCamelCase_							):
            _lowerCamelCase				:   List[str]								=   float(input()							)

      _lowerCamelCase				:   Union[str, Any]								=   int(input("enter the value to interpolate: "							)							)
      _lowerCamelCase				:   Optional[int]								=   (value - x[0]) / (x[1] - x[0])

      # for calculating forward difference table

      for i in range(1				,	lowerCamelCase_							):
            for j in range(n - i							):
                  _lowerCamelCase				:   List[Any]								=   y[j + 1][i - 1] - y[j][i - 1]

      _lowerCamelCase				:   str								=   y[0][0]
      for i in range(1				,	lowerCamelCase_							):
            summ += (ucal(lowerCamelCase_				,	lowerCamelCase_							) * y[0][i]) / math.factorial(lowerCamelCase_							)

      print(F'the value at {value} is {summ}'							)


if __name__ == "__main__":
 main()

'''simple docstring'''






def 		A_       (	_lowerCAmelCase   :    int							):



      """simple docstring"""




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

      if num == 0:
            return "0b0"

      _lowerCamelCase				:   Tuple								=   False

      if num < 0:
            _lowerCamelCase				:   List[Any]								=   True
            _lowerCamelCase				:   int								=   -num

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

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

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


if __name__ == "__main__":
 import doctest

 doctest.testmod()