
"""simple docstring"""





def 	__a     (		__lowerCamelCase = 3,		__lowerCamelCase = 7,		__lowerCamelCase = 100_0000  ):
   UpperCAmelCase_					:					Dict			     =    0
   UpperCAmelCase_					:					List[Any]			     =    1

   for current_denominator in range(1,		limit + 1  ):
      UpperCAmelCase_					:					Dict			     =    current_denominator * numerator // denominator
      if current_denominator % denominator == 0:
         current_numerator -= 1
      if current_numerator * max_denominator > current_denominator * max_numerator:
         UpperCAmelCase_					:					List[Any]			     =    current_numerator
         UpperCAmelCase_					:					Optional[int]			     =    current_denominator
   return max_numerator


if __name__ == "__main__":
    print(solution(numerator=3, denominator=7, limit=1_000_000))




"""simple docstring"""





from __future__ import annotations

import math







def 	__a     (		__lowerCamelCase,		__lowerCamelCase  ):
   UpperCAmelCase_					:					Any			     =    u
   for i in range(1,		__lowerCamelCase  ):
      UpperCAmelCase_					:					int			     =    temp * (u - i)
   return temp







def 	__a     (		):
   UpperCAmelCase_					:					str			     =    int(input("enter the numbers of values: "  )  )
   UpperCAmelCase_					:					list[list[float]]			     =    []
   for _ in range(__lowerCamelCase  ):
      y.append([]  )
   for i in range(__lowerCamelCase  ):
      for j in range(__lowerCamelCase  ):
         y[i].append(__lowerCamelCase  )
         UpperCAmelCase_					:					Tuple			     =    0

   print("enter the values of parameters in a list: "  )
   UpperCAmelCase_					:					Union[str, Any]			     =    list(map(__lowerCamelCase,		input().split()  )  )

   print("enter the values of corresponding parameters: "  )
   for i in range(__lowerCamelCase  ):
      UpperCAmelCase_					:					int			     =    float(input()  )

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

   # for calculating forward difference table

   for i in range(1,		__lowerCamelCase  ):
      for j in range(n - i  ):
         UpperCAmelCase_					:					Union[str, Any]			     =    y[j + 1][i - 1] - y[j][i - 1]

   UpperCAmelCase_					:					Optional[int]			     =    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()


