Problem X
Supervisor

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At large companies it is often quite a lot of work to keep track of who is in charge of what. To try to make things easier, it is common to assign everyone to a supervisor, except the CEO who is their own supervisor. This works well, but then people start quitting their job and others get new jobs at the company, so all this planning has to be updated accordingly.

To save the day, a program that maintains all of this info is needed, something that can tell any given person who their supervisor is.

If an employee quits, their supervisor inherits all of their subordinates. This means if $x$ is the supervisor of $y$, $y$ is the supervisor of $z$ and $y$ quits, $x$ will be the supervisor of $z$ afterwards. When an employee starts at the company they are assigned a supervisor. The CEO of the company will never quit or be replaced, because without them the company would go bankrupt overnight (according to them anyway).

Input

The first line of input contains two integers $n, q$, the number of employees at the start and the number of queries that will follow. It will always hold that $1 \leq n, q \leq 200\, 000$. The employees are numbered $1, 2, \dots , n$ where $1$ is the CEO. Next there is a line with $n$ integers $y_1, y_2, \dots , y_n$. Here $y_i$ gives the number of the employee that is the supervisor of employee number $i$, so $1 \leq y_i \leq n$.

Next there are $q$ lines, each with one query. Each line begins with a +, - or ?. In all cases an integer $x$ will follow on the same line.

If the line begins with a + this means a new employee is starting whose supervisor will be $x$. The number of the new employee is the lowest available number. At the start this number is $n + 1$, but if some employee quits that number becomes available. So if $2, 8$ and $11$ quit the lowest available number is $2$. But if no one quits and $n + 1$ was just taken, the next available number is $n + 2$ and so on.

If the line starts with a - it means that employee number $x$ just quit.

Finally if the line starts with a ? you should output the number of the supervisor of employee $x$, where $x$ will always be the number of an employee who is currently working at the company. There will never be anyone who is their own supervisor, directly or indirectly, except the CEO.

Output

For each query starting with a ? print the number of the supervisor in question on its own line.

Scoring

5 7
1 1 2 3 4
+ 2
? 6
- 2
? 3
? 6
+ 4
? 2

2
1
1
4