**Time limit:**1.00 s**Memory limit:**512 MB

A thief who is on the run can be caught by the police, and then ends up in one of the prisons. A thief who is on the run can also open the gate of a prison. Then every thief in that prison is released from the prison. It would be pointless to open the gate of an empty prison, so that never happens.

You are given a list of $m$ events of the form "thief $x$ has been caught" or "thief $x$ has opened the gate of a prison". Your task is to find a prison assignment that corresponds to the events, or determine that it is not possible.

**Input**

The first input line has three integers $n$, $k$ and $m$: the number of thieves, prisons and events. The thieves and prisons are numbered $1,2,\dots,n$ and $1,2,\dots,k$.

After this, there are $m$ lines that describe the events. Each event is "C $x$" (thief $x$ has been caught) or "O $x$" (thief $x$ opens the gate of a prison).

**Output**

Print a valid prison assignment that consists of $m$ integers: for every event the corresponding prison. If there are no solutions, print "IMPOSSIBLE".

**Example 1**

Input:

`3 2 5`

C 1

C 2

O 3

O 2

C 1

Output:

`1 2 2 1 1`

**Example 2**

Input:

`1 1 1`

O 1

Output:

`IMPOSSIBLE`

**Subtask 1 (8 points)**

- $1 \le n,m \le 10$

- $k=2$

**Subtask 2 (13 points)**

- $1 \le n,k,m \le 10^5$

- $n=k$

**Subtask 3 (14 points)**

- $1 \le n,m \le 10^5$

- $k=2$

**Subtask 4 (18 points)**

- $1 \le n,k,m \le 500$

**Subtask 5 (47 points)**

- $1 \le n,k,m \le 10^5$