Description

Story

A new semester has begun, and everyone must have missed RedCapeFlyingCat! RedCapeFlyingCat wants to play a game with all the students taking Data Structures (that is, you, a penguin).

Problem Statement

people stand in a circle, numbered clockwise. Person holds a flag.

Passing the flag one step means giving it to the next person clockwise.

Process operations:

• insert(k, id): Pass the flag steps. Then add a new person right after the holder (clockwise). The new person takes the flag.
• erase(k): Pass the flag steps. Then pass it more step, and remove the person who just gave it away. Output the removed person.
• print(): Output everyone in the circle, clockwise, starting from the holder.

Explanation

The circle is listed clockwise. The flag holder is in bold.

Initially: .

1. insert(2, 17): The flag moves . Person is added after and takes the flag. Circle: .
2. erase(3): The flag moves , then one more step to . Person is removed, so output 1. Circle: .
3. print(): Output 2 3 17 4 5.

Input

The first line contains two integers and — the initial number of people and the number of operations.

Each of the next lines describes one operation in one of the following formats:

• insert k id
• erase k
• print

Constraints

• in every operation, and the sum of all is at most
• Every inserted satisfies , and all inserted are distinct
• Before each erase, the circle has at least people
• All print() operations output at most numbers in total

Subtasks

Subtask	Constraints	Operations
1	,	insert, erase
2	,	insert, erase, print
3~6	No additional constraints	insert, erase, print

Output

For each erase operation, output one line: the id of the removed person.

For each print operation, output one line: the ids of everyone in the circle, space-separated, clockwise, starting from the flag holder.

Output the lines in the order of the operations.

DO NOT LEAVE TRAILING WHITESPACE AT THE END OF ANY LINE.

Sample Input  Download

Sample Output  Download

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