Pair Cards

AtCoder

IDcodefestival_2016_final_d

Time2000ms

Memory256MB

Difficulty—

Takahashi is playing with $N$ cards. The $i$\-th card has an integer $X_i$ on it. Takahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions: * The integers on the two cards are the same. * The sum of the integers on the two cards is a multiple of $M$. Find the maximum number of pairs that can be created. Note that a card cannot be used in more than one pair. ## Constraints * $2≦N≦10^5$ * $1≦M≦10^5$ * $1≦X_i≦10^5$ ## Input The input is given from Standard Input in the following format: $N$ $M$ $X_1$ $X_2$ $...$ $X_N$ [samples]

Samples

Input #1

7 5
3 1 4 1 5 9 2

Output #1

3

Three pairs $(3,2), (1,4)$ and $(1,9)$ can be created.
It is possible to create pairs $(3,2)$ and $(1,1)$, but the number of pairs is not maximized with this.

Input #2

15 10
1 5 6 10 11 11 11 20 21 25 25 26 99 99 99

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Pair Cards",
    "description": {
      "content": "Takahashi is playing with $N$ cards. The $i$\\-th card has an integer $X_i$ on it. Takahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions: *   The ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "codefestival_2016_final_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is playing with $N$ cards.\nThe $i$\\-th card has an integer $X_i$ on it.\nTakahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions:\n\n*   The ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments