Весенний LIST 2024 - Calculate a limit

Problem C. Calculate a limit ≡

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Author:	A. Klenin	Time limit:	1 sec
Input file:	input.txt	Memory limit:	64 Mb
Output file:	output.txt

Statement

Your program must calculate the value of limx ↦ ∞a₁x + a₂x² + …  + a_nxⁿb₁x + b₂x² + …  + b_nxⁿ.

All coefficients are integers, so the answer must be calculated exactly and presented in the form of irreducible fraction.

Input file format

Input file contains integer n followed first by n integers a₁ a₂… a_n and then by n integers b₁ b₂… b_n.

Output file format

Output file must contain two integers — nominator and denominator of the fraction. If the limit is zero, output integers 0 1. If the limit is infinity, output integers 1 0.

Constraints

1 ≤ n ≤ 100, 0 ≤ a_i, b_i ≤ 10⁹, ∑i (b_i + a_i) > 0

Sample tests

No.	Input file (`input.txt`)	Output file (`output.txt`)
1	`1 2 4`	`1 2`
2	`2 0 1 1 0`	`1 0`