"Bloody Mary"
Description
There is a mixture of water, alcohol and tomato juice in three vessels. The volume ratio of components in the first, second and third vessels is equal a1 : a2 : a3, b1 : b2 : b3 and c1 : c2 : c3 correspondingly.
In what volume ratio is it necessary to take liquids from these vessels in order to create a mixture with a component ratio d1 : d2 : d3?
Input
The input consists of four lines. The first line contains values of parameters a1, a2, a3, the others – values of parameters b1, b2, b3; c1, c2, c3 and d1, d2, d3 correspondingly. All numbers are integers from 0 to 1000; each line contains at least one nonzero value. The values on each line are separated by colons (without spaces).
Output
The output contains a single line with the result. The result has the same format as the input data. If it is impossible to create necessary mixture, the output file should contain a single line with word 'impossible'.
1:0:0
0:1:0
0:0:1
3:2:33:2:3Hint
Your outputs must fit in 64bit integers.
Source
Northeastern Europe 2001, Western Subregion