





'''simple docstring'''







from __future__ import annotations

import math





def   _lowerCAmelCase		(		lowercase   ,      lowercase      )   ->   str:
			__lowerCAmelCase   		=							u
			for i in range(1   ,      _snake_case      ):
						__lowerCAmelCase   		=							temp * (u - i)
			return temp





def   _lowerCAmelCase		(		)   ->   str:
			__lowerCAmelCase   		=							int(input("""enter the numbers of values: """      )      )
			__lowerCAmelCase   		=							[]
			for _ in range(_snake_case      ):
						y.append([]      )
			for i in range(_snake_case      ):
						for j in range(_snake_case      ):
									y[i].append(_snake_case      )
									__lowerCAmelCase   		=							0

			print("""enter the values of parameters in a list: """      )
			__lowerCAmelCase   		=							list(map(_snake_case   ,      input().split()      )      )

			print("""enter the values of corresponding parameters: """      )
			for i in range(_snake_case      ):
						__lowerCAmelCase   		=							float(input()      )

			__lowerCAmelCase   		=							int(input("""enter the value to interpolate: """      )      )
			__lowerCAmelCase   		=							(value - x[0]) / (x[1] - x[0])

			# for calculating forward difference table

			for i in range(1   ,      _snake_case      ):
						for j in range(n - i      ):
									__lowerCAmelCase   		=							y[j + 1][i - 1] - y[j][i - 1]

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

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


if __name__ == "__main__":
	main()






'''simple docstring'''





def 							lowerCamelCase	(					_snake_case	:    int  ,_snake_case	:    int							):





    '''simple docstring'''


    return "\n".join(
        f'''{number} * {i} = {number * i}''' for i in range(1  ,number_of_terms + 1							)							)


if __name__ == "__main__":
 print(multiplication_table(number=5, number_of_terms=10))




