{"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 integers on the two cards are the same.\n*   The sum of the integers on the two cards is a multiple of $M$.\n\nFind the maximum number of pairs that can be created.\nNote that a card cannot be used in more than one pair.\n\n## Constraints\n\n*   $2≦N≦10^5$\n*   $1≦M≦10^5$\n*   $1≦X_i≦10^5$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$\n$X_1$ $X_2$ $...$ $X_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"codefestival_2016_final_d","tags":[],"sample_group":[["7 5\n3 1 4 1 5 9 2","3\n\nThree pairs $(3,2), (1,4)$ and $(1,9)$ can be created.\nIt is possible to create pairs $(3,2)$ and $(1,1)$, but the number of pairs is not maximized with this."],["15 10\n1 5 6 10 11 11 11 20 21 25 25 26 99 99 99","6"]],"created_at":"2026-03-03 11:01:13"}}