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Ural Championship 2006

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J. Lighting in Hogwarts

Time limit: 0.5 second
Memory limit: 64 MB
Corridors of Hogwarts castle are well illuminated: there is a row of magical torches going along each corridor. The torches are situated at small equal intervals, so the illumination of a corridor can be controlled by igniting or putting out some of the torches (of course, using magic).
The Hogwarts caretaker Argus Filch doesn't like it when the illumination is not uniform, because he suspects that rule-breakers may hide in dark places. Your task is to create a uniform illumination of a given brightness.


The first line contains the number N (1 ≤ N ≤ 106) of torches in a corridor. The second line contains the required brightness b, which is an integer in the range from 0 to 100. The brightness is given as a percentage of the maximal brightness (0 corresponds to the state when all torches are put out, 100 is when all torches are ignited).


Output a sequence of N zeros and ones (0 corresponds to an extinguished torch, 1 corresponds to an ignited torch) such that for each segment of the corridor comprising L torches the number of ignited torches differs from L*b/100 by not more than 2.


Problem Author: Idea by Alexander Mironenko, text and programming by Stanislav Vasilyev
Problem Source: The Xth Urals Collegiate Programing Championship, March 24-25, 2006
To submit the solution for this problem go to the Problem set: 1448. Lighting in Hogwarts