Partial Fraction Decomposition

Time Limit: 1 Second    Memory Limit: 32768 KB

It is easy to obtain (6x²-5x-5)/(x³-2x²-x+2) from 1/(x+1) + 2/(x-1) + 3/(x-2). But how about the other way around?

Given a rational function in the form (a₂x²+a₁x+a₀)/(x³+b₂x²+b₁x+b₀) where a_i and b_i are integers for i = 0, 1, 2. If the denominator factors as (x-r₁)(x-r₂)(x-r₃) where r_i's are distinct integers, then these will be the denominators of the partial fraction decomposition. We are looking for a decomposition of the rational function such that

A₁/(x-r₁) + A₂/(x-r₂) + A₃/(x-r₃) = (a₂x²+a₁x+a₀)/(x³+b₂x²+b₁x+b₀)

Input

The input consists of several test cases, each occupying a line with 6 integers in the format:
a₀ a₁ a₂ b₀ b₁ b₂
A case with a₀=a₁=a₂=0 signals the end of input and must not be processed.

Output

For each test case, print in one line the 6 numbers in the format:
r₁ r₂ r₃ A₁ A₂ A₃
Note: It is guaranteed that the decomposition exists for each case, because I obtained the input from output ^_^. It is also guaranteed that r_i's are distinct integers and you must output them in increasing order. However, it is NOT guaranteed that A_i's are integers, and you must output them accurate up to 2 decimal places.

Sample Input

-5 -5 6 2 -1 -2
-5 -3 5 2 -1 -2
0 0 0 1 2 3

Sample Output

-1 1 2 1.00 2.00 3.00
-1 1 2 0.50 1.50 3.00

Submit

Source: Zhejiang University Local Contest 2005