As we all very well know, goats and sheep have been fighting for years about the fields they're grazing. After many fierce fights, the goat leader and the sheep leader decided to meet to try to find a peaceful solution to their problem. After many hours of discussion, they agreed that they will play a game for each field and that the winner will get to graze that field.
The game is played such that a total of
If both the goats and the sheep are playing optimally, for each
Input Specification
The first line of input contains
The following line contains
Output Specification
Output
Scoring
In test cases worth a total of
Sample Input 1
2 9 2
0 1
Sample Output 1
0 1
Explanation for Sample Output 1
When a sheep is playing first, it can play like this: The sheep starts with number 2, after which the goat can say 3 or 4. In both cases, the sheep can say 5, after which the goat can say either 6 or 7. In both cases, the sheep can say 8, after which the goat doesn't have any other choice but 9 and thus losing the game and the field.
Sample Input 2
6 499 5
1 0 0 1 1 0
Sample Output 2
0 1 1 1 1 0
Sample Input 3
10 100 10
0 0 0 1 1 1 1 0 1 1
Sample Output 3
1 1 1 1 1 1 1 1 1 1
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