1D Pawn

AtCoder

IDabc257_b

Time2000ms

Memory256MB

Difficulty—

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: $N$ $K$ $Q$ $A_1$ $A_2$ $\ldots$ $A_K$ $L_1$ $L_2$ $\ldots$ $L_Q$ [samples]

Samples

Input #1

5 3 5
1 3 4
3 3 1 1 2

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.

Input #2

2 2 2
1 2
1 2

Output #2

1 2

Input #3

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

Output #3

2 5 6 7 9 10

API Response (JSON)

{
  "problem": {
    "name": "1D Pawn",
    "description": {
      "content": "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 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc257_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ squares, indexed Square $1$, Square $2$, …, Square $N$, arranged in a row from left to right.  \nAlso, there are $K$ pieces. The $i$\\-th piece from the left is initially placed on Square ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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