Many Oranges

AtCoder
IDabc195_b
Time2000ms
Memory256MB
Difficulty
We have many oranges. It is known that every orange weighs between $A$ and $B$ grams, inclusive. (An orange can have a non-integer weight.) We chose some of those oranges, and their total weight was exactly $W$ kilograms. Find the minimum and maximum possible numbers of oranges chosen. If no set of oranges can weigh exactly $W$ kilograms in total, report that fact. ## Constraints * $1 \leq A \leq B \leq 1000$ * $1 \leq W \leq 1000$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $A$ $B$ $W$ [samples]
Samples
Input #1
100 200 2
Output #1
10 20

Here, one range weighs between $100$ and $200$ grams (inclusive).

*   If we choose $10$ $200$\-gram oranges, their total weight will be exactly $2$ kilograms.
*   If we choose $20$ $100$\-gram oranges, their total weight will be exactly $2$ kilograms.

With less than $10$ oranges or more than $20$ oranges, the total weight will never be exactly $2$ kilograms, so the minimum and maximum possible numbers of oranges chosen are $10$ and $20$, respectively.
Input #2
120 150 2
Output #2
14 16

Here, one range weighs between $120$ and $150$ grams (inclusive).

*   If we choose $10$ $140$\-gram oranges and $4$ $150$\-gram oranges, for example, their total weight will be exactly $2$ kilograms.
*   If we choose $8$ $120$\-gram oranges and $8$ $130$\-gram oranges, for example, their total weight will be exactly $2$ kilograms.

With less than $14$ oranges or more than $16$ oranges, the total weight will never be exactly $2$ kilograms, so the minimum and maximum possible numbers of oranges chosen are $14$ and $16$, respectively.
Input #3
300 333 1
Output #3
UNSATISFIABLE

Here, one range weighs between $300$ and $333$ grams (inclusive).
No set of oranges of this kind can weigh exactly $1$ kilograms in total.
API Response (JSON)
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      "statement_type": "Markdown",
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