Usual Color Ball Problems

AtCoder
IDabc337_f
Time2000ms
Memory256MB
Difficulty
You are given positive integers $N$, $M$, $K$, and a sequence of positive integers of length $N$, $(C_1, C_2, \ldots, C_N)$. For each $r = 0, 1, 2, \ldots, N-1$, print the answer to the following problem. > There is a sequence of $N$ colored balls. For $i = 1, 2, \ldots, N$, the color of the $i$\-th ball from the beginning of the sequence is $C_i$. Additionally, there are $M$ empty boxes numbered $1$ to $M$. > Determine the total number of balls in the boxes after performing the following steps. > > * First, perform the following operation $r$ times. > * Move the frontmost ball in the sequence to the end of the sequence. > * Then, repeat the following operation as long as at least one ball remains in the sequence. > * If there is a box that already contains at least one but fewer than $K$ balls of the same color as the frontmost ball in the sequence, put the frontmost ball into that box. > * If there is no such box, > * If there is an empty box, put the frontmost ball into the one with the smallest box number. > * If there are no empty boxes, eat the frontmost ball without putting it into any box. ## Constraints * All input values are integers. * $1 \leq N \leq 2 \times 10^5$ * $1 \leq M, K \leq N$ * $1 \leq C_i \leq N$ ## Input The input is given from Standard Input in the following format: $N$ $M$ $K$ $C_1$ $C_2$ $\ldots$ $C_N$ [samples]
Samples
Input #1
7 2 2
1 2 3 5 2 5 4
Output #1
3
3
3
4
4
3
2

For example, let us explain the procedure for $r = 1$. First, perform the operation "Move the frontmost ball in the sequence to the end of the sequence" once, and the sequence of ball colors becomes $(2, 3, 5, 2, 5, 4, 1)$. Then, proceed with the operation of putting balls into boxes as follows:

*   First operation: The color of the frontmost ball is $2$. There is no box with at least one but fewer than two balls of color $2$, so put the frontmost ball into the empty box with the smallest box number, box $1$.
*   Second operation: The color of the frontmost ball is $3$. There is no box with at least one but fewer than two balls of color $3$, so put the frontmost ball into the empty box with the smallest box number, box $2$.
*   Third operation: The color of the frontmost ball is $5$. There is no box with at least one but fewer than two balls of color $5$ and no empty boxes, so eat the frontmost ball.
*   Fourth operation: The color of the frontmost ball is $2$. There is a box, box $1$, with at least one but fewer than two balls of color $2$, so put the frontmost ball into box $1$.
*   Fifth operation: The color of the frontmost ball is $5$. There is no box with at least one but fewer than two balls of color $5$ and no empty boxes, so eat the frontmost ball.
*   Sixth operation: The color of the frontmost ball is $4$. There is no box with at least one but fewer than two balls of color $4$ and no empty boxes, so eat the frontmost ball.
*   Seventh operation: The color of the frontmost ball is $1$. There is no box with at least one but fewer than two balls of color $1$ and no empty boxes, so eat the frontmost ball.

The final total number of balls in the boxes is $3$, so the answer to the problem for $r = 1$ is $3$.
Input #2
20 5 4
20 2 20 2 7 3 11 20 3 8 7 9 1 11 8 20 2 18 11 18
Output #2
14
14
14
14
13
13
13
11
8
9
9
11
13
14
14
14
14
14
14
13
API Response (JSON)
{
  "problem": {
    "name": "Usual Color Ball Problems",
    "description": {
      "content": "You are given positive integers $N$, $M$, $K$, and a sequence of positive integers of length $N$, $(C_1, C_2, \\ldots, C_N)$. For each $r = 0, 1, 2, \\ldots, N-1$, print the answer to the following prob",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc337_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given positive integers $N$, $M$, $K$, and a sequence of positive integers of length $N$, $(C_1, C_2, \\ldots, C_N)$. For each $r = 0, 1, 2, \\ldots, N-1$, print the answer to the following prob...",
      "is_translate": false,
      "language": "English"
    }
  ]
}
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