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Alice is a card dealer at the poker table in the 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.

## Task

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 the top-most card as the 0-th card. in our example above, if *k* = 3, then the answer is "3 1 5"

## Input

The first line of the input consists of two integers *m* and *k*, where 0 < *k* < *m*-1, and 3 ≤ *m* ≤ 1,000,000. This is followed (in the same line) by the sequence of moves. The last character in the input is the period ".", indicating the end of input.

## Output

The output consists of 3 integers, representing the (*k*-1)-th, *k*-th and (*k*+1)-th cards from the top of the deck after the entire sequence of moves have been applied.

## Sample Input 1

6 3 ABBABA.

## Sample Output 1

3 1 5

## Explanation for Sample Output 1

Initially, the deck is arranged as such: 0 1 2 3 4 5

After each subsequent move, the deck will be arranged as such:

A: 1 2 3 4 5 0B: 1 3 4 5 0 2

B: 1 4 5 0 2 3

A: 4 5 0 2 3 1

B: 4 0 2 3 1 5

A: 0 2 3 1 5 4

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 100 | 10 | 1s | 64MB | Average |

2 | 0 | 1 | 1s | 64MB | Average |

### Judge Compile Command

g++-7 ans.cpp -o card -Wall -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512