102571: [AtCoder]ABC257 B - 1D Pawn

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

问题描述

有$N$个方格，按照从左到右的顺序编号为 Square $1$，Square $2$，…，Square $N$。
此外，有$K$个棋子。最左边的第$i$个棋子初始放置在 Square $A_i$。
现在，我们要对它们进行$Q$次操作。 第$i$次操作如下：

• 如果从左边数的第$L_i$个棋子在其最右侧的方格上，则什么也不做。
• 否则，如果右边相邻的方格上没有棋子，将从左边数的第$L_i$个棋子向右移动一个方格；否则，什么也不做。

在进行完$Q$次操作后，对于每$i=1,2,\ldots,K$，输出从左边数的第$i$个棋子所在的方格的编号。

限制条件

• $1\leq K\leq N\leq 200$
• $1\leq A_1<A_2<\cdots<A_K\leq N$
• $1\leq Q\leq 1000$
• $1\leq L_i\leq K$
• 输入中的所有值都是整数。

输入

输入通过标准输入给出，格式如下：

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

输出

在一行中打印$K$个整数，之间用空格隔开。 第$i$个整数应该是进行完$Q$次操作后，从左边数的第$i$个棋子所在的方格的编号。

样例输入 1

5 3 5
1 3 4
3 3 1 1 2

样例输出 1

2 4 5

起始时，棋子在Squares $1$，$3$和$4$上。按照以下方式对它们进行操作：

• 从左边数的第$3$个棋子在Square $4$上。 这不是最右侧的方格，且右边相邻的方格上没有棋子，所以将从左边数的第$3$个棋子移动到Square $5$。 现在，棋子在Squares $1$，$3$和$5$上。
• 从左边数的第$3$个棋子在Square $5$上。 这是最右侧的方格，所以什么也不做。 棋子仍然在Squares $1$，$3$和$5$上。
• 从左边数的第$1$个棋子在Square $1$上。 这不是最右侧的方格，且右边相邻的方格上没有棋子，所以将从左边数的第$1$个棋子移动到Square $2$。 现在，棋子在Squares $2$，$3$和$5$上。
• 从左边数的第$1$个棋子在Square $2$上。 这不是最右侧的方格，但右边相邻的方格（Square $3$）上有一个棋子，所以什么也不做。 棋子仍然在Squares $2$，$3$和$5$上。
• 从左边数的第$2$个棋子在Square $3$上。 这不是最右侧的方格，且右边相邻的方格上没有棋子，所以将从左边数的第$2$个棋子移动到Square $4$； 现在，棋子仍然在Squares $2$，$4$和$5$上。

因此，在进行完$Q$次操作后，棋子在Squares $2$，$4$和$5$上，因此应按顺序打印$2$，$4$和$5$，之间用空格隔开。

样例输入 2

2 2 2
1 2
1 2

样例输出 2

1 2

样例输入 3

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

样例输出 3

2 5 6 7 9 10