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:
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.
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)~.
Second 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.
Sample Input 1
5 3 1
Sample Output 1
Sample Input 2
5 3 2
Sample Output 2
Sample Input 3
5 4 5
Sample Output 3