Kolo

During meetings of young mathematicians a frequent pastime is the Prime Number Circle. For this
task, we refer to mathematicians in the circle with numbers 1 to N.
Before the game starts we first draw \(N-1\) circles and one square on the pavement arranged in a big
circle. The player numbered 1 stands in the square. All other players stand in the circles, starting with
the player 2 in a counterclockwise fashion facing towards the middle of the big circle.
The game consists of K rounds. In the \(i-th\) round the person standing in the square jumps up, says "It's
me!" and then swaps places with the person standing on his right side \(p_{k}\) times, where \(p_{k}\) is the \(k-th\)
prime. For example for \(N = 5\) and \(K = 3\) the following three rounds occur:
1. round:
2. round:
3. round:
Write a program that will for given N, K and A determine the neighbours of the player numbered A at
the end of the game.

The first and only line contains three integers N, K and A. (\(1 \le A \le N\)), the number of players, rounds
and the selected player.
SCORING
Test data is divided into four groups each worth 25 points, with the following constraints:
First group: (\(3 \le N \le 1\,000\), \(1 \le K \le 1\,000\)).
Secong group: (\(3 \le N \le 1\,000\), \(1 \le K \le 50\,000\)).
Third group: (\(3 \le N \le 50\,000\), \(1 \le K \le 50\,000\)).
Fourth group: (\(3 \le N \le 5\,000\,000\), \(1 \le K \le 500\,000\)).

The first and only line of output should contain two integers, the numbers on the right and left
neighbours of the player numbered A at the end of the game.

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출처 COI 2010