Shuffle and mod K

AtCoder

IDagc065_a

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence $A=(A_1,A_2,\dots,A_N)$ of length $N$. You can rearrange $A$ freely. Find the maximum value that $\sum_{i=1}^{N-1} ((A_{i+1} - A_i) \bmod K)$ can take after rearranging. Here, $x \bmod K$ denotes the integer $y$ such that $0 \le y < K$ and $x - y$ is a multiple of $K$. For example, $-3 \bmod 8 = 5$, and $9 \bmod 6 = 3$. ## Constraints * $2 \le N \le 2 \times 10^5$ * $1 \le K \le 10^9$ * $0 \le A_i < K$ ## Input The input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

3 4
0 1 2

Output #1

6

One optimal solution is to rearrange $A$ into $(2,1,0)$ to achieve $(1 - 2) \bmod 4 + (0 - 1) \bmod 4 = 3 + 3 = 6$.

Input #2

7 123
11 34 56 0 32 100 78

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Shuffle and mod K",
    "description": {
      "content": "You are given an integer sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$. You can rearrange $A$ freely. Find the maximum value that $\\sum_{i=1}^{N-1} ((A_{i+1} - A_i) \\bmod K)$ can take after rearrangi",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc065_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$.\nYou can rearrange $A$ freely. Find the maximum value that $\\sum_{i=1}^{N-1} ((A_{i+1} - A_i) \\bmod K)$ can take after rearrangi...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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