Add to Make a Permutation

AtCoder

IDarc169_d

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence $A=(A_1,A_2,\cdots,A_N)$ of length $N$. Each element of $A$ is an integer between $0$ and $N-1$, inclusive. You can perform the following operation zero or more times: * Choose exactly $M$ elements from $A$. Then, increase the value of each chosen element by $1$. Now, if some elements have the values of $N$, change those values to $0$. Your goal is to make $A$ a permutation of $(0,1,\cdots,N-1)$. Determine if the goal is achievable. If it is, find the minimum number of operations required. ## Constraints * $2 \leq N \leq 250000$ * $1 \leq M \leq N-1$ * $0 \leq A_i \leq N-1$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

3 2
0 1 1

Output #1

2

You can operate as follows to achieve the goal in two operations:

*   Initial state: $A=(0,1,1)$.
*   First operation: Choose $A_1$ and $A_2$, making $A=(1,2,1)$.
*   Second operation: Choose $A_2$ and $A_3$, making $A=(1,0,2)$.

You cannot achieve the goal in fewer than two operations, so the answer is $2$.

Input #2

5 2
0 4 2 3 1

Output #2

Input #3

4 2
0 0 1 2

Output #3

\-1

Input #4

20 15
5 14 18 0 8 5 0 10 6 5 11 2 10 10 17 9 8 14 4 4

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Add to Make a Permutation",
    "description": {
      "content": "You are given an integer sequence $A=(A_1,A_2,\\cdots,A_N)$ of length $N$. Each element of $A$ is an integer between $0$ and $N-1$, inclusive. You can perform the following operation zero or more times",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc169_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence $A=(A_1,A_2,\\cdots,A_N)$ of length $N$. Each element of $A$ is an integer between $0$ and $N-1$, inclusive.\nYou can perform the following operation zero or more times...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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