P12404 "CZOI-R3" Cute Lambs

A farmer has $N$ lambs. They are kept in **a single consecutive row** of $N$ pens. One day, $x$ different lambs got sick. Every night, each lamb that is already infected will randomly infect **one of its adjacent** lambs. Also, the same lamb may be infected multiple times. The $i$-th lamb is adjacent only to lambs $i-1$ and $i+1$. In particular, the only adjacent lamb of lamb $1$ is $2$, and the only adjacent lamb of lamb $N$ is $N-1$. After $T$ days (i.e. after $T$ rounds of infection), the farmer finally discovers this. He is very anxious and urgently wants to know: among all possible situations, what are the **maximum** and **minimum** possible numbers of infected lambs now.

The first line contains $3$ integers $N, T, x$.

Output $2$ integers in the first line, representing the **maximum** and **minimum** possible numbers of infected lambs. If at least one number in your output is correct, you will get $50\%$ of the score for that test point. If you cannot output one of them, please use $0$ instead, otherwise you will not get any points.

**[Sample Explanation #1]** After the first round of infection, both lambs will be infected, so the **maximum** and **minimum** numbers of infected lambs are both $2$. **[Constraints]** **This problem uses bundled tests.** - Subtask #1 ($20\text{ pts}$): $N, T \le 20$. - Subtask #2 ($20\text{ pts}$): $N \le 20$. - Subtask #3 ($20\text{ pts}$): $x = 1$. - Subtask #4 ($40\text{ pts}$): no special constraints. For $100\%$ of the testdata, $2 \le N, T \le 10^9$, $1 \le x \le N$. Translated by ChatGPT 5