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2 초 512 MB 2 2 2 100.000%

문제

Alice is a card dealer at the poker table in newly opened ResortWorld casino. As a strange personal quirk, she has two ways of moving a card when she shuffles the deck:

  • A: She takes the card at the top of the deck and moves it to the bottom.
  • B: She takes the second card from the top of the deck and moves it to the bottom.

Initially, Alice has m cards (note that m can be very much more than the standard 52 cards found in a deck) which are labeled consecutively: the card at the top is labeled 0 and the card at the bottom is labeled m − 1. Consider a sequence of moves like:

ABBABA

The table below shows the deck after each move in the sequence is applied.

Next move A B B A B A  
Current
deck
arrangement
0 1 1 1 4 4 0
1 2 3 4 5 0 2
2 3 4 5 0 2 3
3 4 5 0 2 3 1
4 5 0 2 3 1 5
5 0 2 3 1 5 4

In this question we want to know: given a sequence of moves and a k, where 0 < k < m−1, what is the label of the (k − 1)–th, k–th and (k + 1)–th cards from the top of the deck after the entire sequence is applied? Here, we treat top-most card as the 0–th card. In our example above, if k = 3, then the answer is “3 1 5”.

입력

Your program must read from the standard input. The input consists of m and k, where 0 < k < m − 1, and 3 ≤ m ≤ 1, 000, 000, and the sequence of moves in a single line. The last character in the input is the period “.”, indicating the end of input. The total number of moves is at least 1 and at most 100,000.

출력

Your program must write to the standard output the (k − 1)–th, k–th and (k + 1)–th cards from the top of the deck after the entire sequence of card moves have been applied.

예제 입력 1

6 3 ABBABA.

예제 출력 1

3 1 5