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.

Input Specification

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: $(3\le N\le 1000,1\le K\le 1000)$.

Second group: $(3\le N\le 1000,1\le K\le 50000)$.

Third group: $(3\le N\le 50000,1\le K\le 50000)$.

Fourth group: $(3\le N\le 5000000,1\le K\le 500000)$.

Output Specification

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

3 5

Sample Input 2

5 3 2

Sample Output 2

5 4

Sample Input 3

5 4 5

Sample Output 3

3 2