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 $i=1,2,\ldots,K$.

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.

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.

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

见题面 Input 部分

见题面 Output 部分