9618: ABC257 —— B - 1D Pawn
[Creator : ]
Description
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 $i=1,2,\ldots,K$.
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:
```
$N$ $K$ $Q$
$A_1$ $A_2$ $\ldots$ $A_K$
$L_1$ $L_2$ $\ldots$ $L_Q$
```
```
$N$ $K$ $Q$
$A_1$ $A_2$ $\ldots$ $A_K$
$L_1$ $L_2$ $\ldots$ $L_Q$
```
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.
- $1\leq A_1 < A_2 < \cdots < A_K\leq N$
- $1\leq Q\leq 1000$
- $1\leq L_i\leq K$
- All values in input are integers.
Sample 1 Input
5 3 5
1 3 4
3 3 1 1 2
Sample 1 Output
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 55, so 2, 4, and 5 should be printed in this order, with spaces in between.
Sample 2 Input
2 2 2
1 2
1 2
Sample 2 Output
1 2
Sample 3 Input
10 6 9
1 3 5 7 8 9
1 2 3 4 5 6 5 6 2
Sample 3 Output
2 5 6 7 9 10