There are n thieves and k prisons. A thief is either on the run or caught in a prison. Initially all thieves are on the run.

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