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C - Large RPS Tournament /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

r-l2 のべき乗であるような l, r について、番号が l 以上 r 未満の参加者による大会を開いたとき、勝者は次のようにして決定されます。

• r-l=1 であるとき（つまり、参加者がただ一人であるとき）、勝者は l とする。
• r-l\geq 2 であるとき、m=(l+r)/2 として、l 以上 m 未満の参加者による大会と、m 以上 r 未満の参加者による大会を開催する。それぞれの勝者が a, b であるとき、ab がじゃんけんをして勝ったほうを勝者とする。あいこの場合 a を勝者とする。

### 注意

• a\text{ mod } bab で割ったあまりを表す
• じゃんけんの勝敗は次のように決められる
• 同じ手同士はあいこである
• RS に勝つ
• PR に勝つ
• SP に勝つ

### 制約

• 1 \leq n,k \leq 100
• sR, P, S のみからなる長さ n の文字列

### 入力

n k
s


### 入力例 1

3 2
RPS


### 出力例 1

P

• 番号が 0 以上 2 未満の参加者による大会の勝者の得意な手は P です。
• 番号が 2 以上 4 未満の参加者による大会の勝者の得意な手は R です。
• 番号が 0 以上 4 未満の参加者による大会の勝者の得意な手は P です。

よって、答えは P となります。

   P
┌─┴─┐
P   R
┌┴┐ ┌┴┐
R P S R


### 入力例 2

11 1
RPSSPRSPPRS


### 出力例 2

P


### 入力例 3

1 100
S


### 出力例 3

S


Score : 500 points

### Problem Statement

To decide which is the strongest among Rock, Paper, and Scissors, we will hold an RPS tournament. There are 2^k players in this tournament, numbered 0 through 2^k-1. Each player has his/her favorite hand, which he/she will use in every match.

A string s of length n consisting of R, P, and S represents the players' favorite hands. Specifically, the favorite hand of Player i is represented by the ((i\text{ mod } n) + 1)-th character of s; R, P, and S stand for Rock, Paper, and Scissors, respectively.

For l and r such that r-l is a power of 2, the winner of the tournament held among Players l through r-1 will be determined as follows:

• If r-l=1 (that is, there is just one player), the winner is Player l.
• If r-l\geq 2, let m=(l+r)/2, and we hold two tournaments, one among Players l through m-1 and the other among Players m through r-1. Let a and b be the respective winners of these tournaments. a and b then play a match of rock paper scissors, and the winner of this match - or a if the match is drawn - is the winner of the tournament held among Players l through r-1.

Find the favorite hand of the winner of the tournament held among Players 0 through 2^k-1.

### Notes

• a\text{ mod } b denotes the remainder when a is divided by b.
• The outcome of a match of rock paper scissors is determined as follows:
• If both players choose the same hand, the match is drawn;
• R beats S;
• P beats R;
• S beats P.

### Constraints

• 1 \leq n,k \leq 100
• s is a string of length n consisting of R, P, and S.

### Input

Input is given from Standard Input in the following format:

n k
s


### Output

Print the favorite hand of the winner of the tournament held among Players 0 through 2^k-1, as R, P, or S.

### Sample Input 1

3 2
RPS


### Sample Output 1

P

• The favorite hand of the winner of the tournament held among Players 0 through 1 is P.
• The favorite hand of the winner of the tournament held among Players 2 through 3 is R.
• The favorite hand of the winner of the tournament held among Players 0 through 3 is P.

Thus, the answer is P.

   P
┌─┴─┐
P   R
┌┴┐ ┌┴┐
R P S R


### Sample Input 2

11 1
RPSSPRSPPRS


### Sample Output 2

P


### Sample Input 3

1 100
S


### Sample Output 3

S