Problem - Teleporters Path

Problem: A game has $n$ levels with $m$ one-way teleporters. You start at level $1$ and want to reach level $n$ using each teleporter exactly once.

Link: CSES 1693

Constraints:

• $2 \leq n \leq 10^5$
• $1 \leq m \leq 2 \times 10^5$

Output: A sequence of levels, or "IMPOSSIBLE" if no valid path exists.

Note: This is a directed Euler path problem, not a circuit.