KOLO

문제

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_i times, where p_i is the i-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. 

입력

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

 

출력

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