findTheFormula

Consider a sequence in which each element is obtained from the previous one by applying some function f to it. Given three consecutive elements from this sequence as an array seq, your task is to find and return the function f used to build it.

Function f in the format k*n[+/-]b. If b is equal to zero, it should be omitted. If the absolute value of k is 1, it should be omitted as well.

It is guaranteed that the given function is not a constant and it not an identity function.

Example:

• For seq = [7,8,9], the output should be findTheFormula(seq) ="n+1".

Let f = n + 1. In this case f(7) = 8, and f(8) = 9, which coincides with the given elements. Thus, the answer is "n+1".

Input/Output:

• [execution time limit] 0.5 seconds

• [input] array.integer seq
  seq.length = 3,
  -106 ≤ seq[i] ≤ 106.

• [output] string

  Function f in the format kn[+-]b. If b is equal to zero, it should be omitted. If the absolute value of k is 1, it should be omitted as well.