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Contest: Task: Related: TaskA TaskC

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

Print $K$ 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 1

5 3 5
1 3 4
3 3 1 1 2

Sample Output 1

2 4 5

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.

Sample Input 2

2 2 2
1 2
1 2

Sample Output 2

1 2

Sample Input 3

10 6 9
1 3 5 7 8 9
1 2 3 4 5 6 5 6 2

Sample Output 3

2 5 6 7 9 10