P7510 Bell Solution Suffix

Problem: constructing number pairs.

Split the integers $1 \sim 2n$ into $n$ ordered pairs $(a_i, b_i)$ ($1 \le i \le n$). You need to make sure that for every positive integer $i$ not greater than $n$, we have $a_i - b_i = i$. Given $n$, please provide one construction. If there is no solution, output `-1 0`.

One line with one positive integer $n$.

If there is no solution, output one line with two integers `-1 0`. Otherwise output $n$ lines, each with two positive integers within $1 \sim 2n$, representing $(a_i, b_i)$. You need to ensure that the $n$ pairs $(a_i, b_i)$, in order of increasing $a_i - b_i$, together form a permutation of the integers $1 \sim 2n$.

**Sample Explanation** For the first sample, obviously there is no solution. For the second sample, the sample output gives a feasible construction. **Constraints and Notes** **This problem uses bundled tests.** $\texttt{Subtask 1 (20 pts)}$: $n \le 5$. $\texttt{Subtask 2 (20 pts)}$: $n \le 10 ^ 5$. $\texttt{Subtask 3 (30 pts)}$: $n$ is prime. $\texttt{Subtask 4 (30 pts)}$: no special restrictions. For $100\%$ of the data, $1 \le n \le 10^6$. This problem is meant to train mathematical thinking and construction skills, but it is not suitable for OI contests. [CoOI Round 1](https://www.luogu.com.cn/contest/43016) Problem B. Translated by ChatGPT 5