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Description

Time Limit: 2 sec / Memory Limit: 1024 MB

Score :

200

points

Problem Statement

There are

N

squares, indexed Square

1

, Square

2

, …, Square

N

, arranged in a row from left to right.
Also, there are

K

pieces. The

i

-th piece from the left is initially placed on Square

A_i

.
Now, we will perform

Q

operations against them. The

i

-th operation is as follows:

If the $L_i$ -th piece from the left is on its rightmost square, do nothing.
Otherwise, move the $L_i$ -th piece from the left one square right if there is no piece on the next square on the right; if there is, do nothing.

Print the index of the square on which the

i

-th piece from the left is after the

Q

operations have ended, for each

i=1,2,\ldots,K

Constraints

$1\leq K\leq N\leq 200$
$1\leq A_1<A_2<\cdots<A_K\leq N$
$1\leq Q\leq 1000$
$1\leq L_i\leq K$
All values in input are integers.

Input

Input is given from Standard Input in the following format:

 $N$  $K$  $Q$  $A_1$  $A_2$  $\ldots$  $A_K$  $L_1$  $L_2$  $\ldots$  $L_Q$

Output

K

integers in one line, with spaces in between. The

i

-th of them should be the index of the square on which the

i

-th piece from the left is after the

Q

operations have ended.

Sample Input Copy

5 3 5
1 3 4
3 3 1 1 2

Sample Output Copy

2 4 5

HINT

At first, the pieces are on Squares $1$ , $3$ , and $4$ . The operations are performed against them as follows:

The $3$ -rd piece from the left is on Square $4$ . This is not the rightmost square, and the next square on the right does not contain a piece, so move the $3$ -rd piece from the left to Square $5$ . Now, the pieces are on Squares $1$ , $3$ , and $5$ .
The $3$ -rd piece from the left is on Square $5$ . This is the rightmost square, so do nothing. The pieces are still on Squares $1$ , $3$ , and $5$ .
The $1$ -st piece from the left is on Square $1$ . This is not the rightmost square, and the next square on the right does not contain a piece, so move the $1$ -st piece from the left to Square $2$ . Now, the pieces are on Squares $2$ , $3$ , and $5$ .
The $1$ -st piece from the left is on Square $2$ . This is not the rightmost square, but the next square on the right (Square $3$ ) contains a piece, so do nothing. The pieces are still on Squares $2$ , $3$ , and $5$ .
The $2$ -nd piece from the left is on Square $3$ . This is not the rightmost square, and the next square on the right does not contain a piece, so move the $2$ -nd piece from the left to Square $4$ ; Now, the pieces are still on Squares $2$ , $4$ , and $5$ .

Thus, after the $Q$ operations have ended, the pieces are on Squares $2$ , $4$ , and $5$ , so $2$ , $4$ , and $5$ should be printed in this order, with spaces in between.

Source/Category

AtCoder

2356: 1D Pawn