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USU Championship 2006

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E. Film Rating

Time limit: 1.0 second
Memory limit: 64 MB
Denis is an expert film fan. He goes to a cinema to watch all films which get high rating at his favorite film-fan Web site. Usually he is satisfied with films, but today, after yet another contest at the Petrozavodsk Training Camp, he has watched a film narrating the hard lot of narfs, scrunts, and tartutics. Denis didn't like the film at all. Now he wants to lower the rating of this film at the Web site, so that other film fans won't go to a cinema to watch such a dreadful film.
The rating of a film is determined as follows: each site visitor may estimate a film and give it a mark, which is an integer from 1 to 10. A film's rating is the arithmetic average of the marks given by visitors rounded to one fractional digit (for example, 7.54 is rounded to 7.5, and 7.55 and 7.58 are rounded to 7.6). Denis can see that now the film has been estimated by N visitors and its rating is X. He wants the rating to become not greater than Y. It remains to determine how many times Denis must estimate the film in order to achieve this goal.


The only line contains the numbers X, Y, and N. The numbers X and Y are given with one fractional digit. 1 ≤ XY ≤ 10. 1 ≤ N ≤ 106.


Output the minimal number of votes that is needed to guarantee that the rating becomes not greater than Y. If it is impossible to do this, then output “Impossible”.


9.5 2.0 12
Problem Author: Vladimir Yakovlev
Problem Source: The XIth USU Programing Championship, October 7, 2006
To submit the solution for this problem go to the Problem set: 1484. Film Rating