P6188 [NOI Online #1 Junior] Stationery Order

Xiaoming’s class has a total class fund of $n$ yuan. The students plan to use the fund to collectively buy $3$ kinds of items: 1. Compass, $7$ yuan each. 2. Pen, $4$ yuan each. 3. Notebook, $3$ yuan each. Xiaoming is responsible for ordering the stationery. Let the ordered quantities of compasses, pens, and notebooks be $a, b, c$ respectively. His ordering rules, in order, are: 1. The $n$ yuan must be spent exactly, i.e. $7a + 4b + 3c = n$. 2. Subject to the above condition, the number of complete sets should be as large as possible, i.e. $\min(a, b, c)$ should be as large as possible. 3. Subject to the above conditions, the total number of items should be as large as possible, i.e. $a + b + c$ should be as large as possible. Please help Xiaoming find the optimal plan that satisfies the conditions. It can be proven that if a plan exists, then the optimal plan is unique.

The input contains only one line with one integer, representing the class fund amount $n$.

If there is no solution, output $-1$. Otherwise, output one line with three integers $a, b, c$ separated by spaces, representing the numbers of compasses, pens, and notebooks.

#### Explanation of Sample Input/Output 3 $a = 2, b = 4, c = 1$ is also a plan that satisfies conditions $1$ and $2$, but for condition $3$, this plan buys only $7$ items in total, which is worse than the plan $a = 1, b = 2, c = 6$. #### Constraints - For test points $1 \sim 6$, $n \leq 14$ is guaranteed. - For test points $7 \sim 12$, $n$ is guaranteed to be a multiple of $14$. - For test points $13 \sim 18$, $n \leq 100$ is guaranteed. - For all test points, $0 \leq n \leq 10^5$ is guaranteed. Translated by ChatGPT 5