1639. Prime Number Circle

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:

The first and only line contains three integers `N`, `K` and `A` (`1\ ≤\ A\ ≤\ N`, `3\ ≤\ N\ ≤\ 5\ 000\ 000`, `1\ ≤\ K\ ≤\ 500\ 000`), the number of players, rounds and the selected player.

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.

5 3 1

3 5

5 3 2

5 4

5 4 5 

3 2