C. Number of Apartments

Codeforces

IDCF10279C

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Recently a new building with a new layout was constructed in Monocarp's hometown. According to this new layout, the building consists of three types of apartments: three-room, five-room, and seven-room apartments. It's also known that each room of each apartment has exactly one window. In other words, a three-room apartment has three windows, a five-room — five windows, and a seven-room — seven windows. Monocarp went around the building and counted $n$ windows. Now he is wondering, how many apartments of each type the building may have. Unfortunately, Monocarp only recently has learned to count, so he is asking you to help him to calculate the possible quantities of three-room, five-room, and seven-room apartments in the building that has $n$ windows. If there are multiple answers, you can print any of them. The first line contains one integer $n$ ($1 <= n <= 10^(18)$) — the number of windows in the building. If a building with the new layout and the given number of windows just can't exist, print $-1$. Otherwise, print three non-negative integers — the possible number of three-room, five-room, and seven-room apartments. If there are multiple answers, print any of them. In the first sample, one of possible answers is $2$ three-room apartments, $2$ five-room apartments, and $2$ seven-room apartments. So the number of windows is equal to $2 dot.op 3 + 2 dot.op 5 + 2 dot.op 7 = 30$. ## Input The first line contains one integer $n$ ($1 <= n <= 10^(18)$) — the number of windows in the building. ## Output If a building with the new layout and the given number of windows just can't exist, print $-1$.Otherwise, print three non-negative integers — the possible number of three-room, five-room, and seven-room apartments. If there are multiple answers, print any of them. [samples] ## Note In the first sample, one of possible answers is $2$ three-room apartments, $2$ five-room apartments, and $2$ seven-room apartments. So the number of windows is equal to $2 dot.op 3 + 2 dot.op 5 + 2 dot.op 7 = 30$.

**Definitions** Let $ n \in \mathbb{Z} $ be the total number of windows, with $ 1 \leq n \leq 10^{18} $. Let $ x, y, z \in \mathbb{Z}_{\geq 0} $ denote the number of three-room, five-room, and seven-room apartments, respectively. **Constraints** $$ 3x + 5y + 7z = n $$ **Objective** Find any non-negative integer solution $ (x, y, z) $ to the equation above. If no such solution exists, output $-1$.

API Response (JSON)

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    "description": {
      "content": "Recently a new building with a new layout was constructed in Monocarp's hometown. According to this new layout, the building consists of three types of apartments: three-room, five-room, and seven-roo",
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    "platform": "Codeforces",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 262144
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      "content": "Recently a new building with a new layout was constructed in Monocarp's hometown. According to this new layout, the building consists of three types of apartments: three-room, five-room, and seven-roo...",
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      "statement_type": "Markdown",
      "content": "**Definitions**  \nLet $ n \\in \\mathbb{Z} $ be the total number of windows, with $ 1 \\leq n \\leq 10^{18} $.  \nLet $ x, y, z \\in \\mathbb{Z}_{\\geq 0} $ denote the number of three-room, five-room, and sev...",
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Full JSON Raw Segments