P2404 Decomposition of a Natural Number

Any natural number $n$ greater than $1$ can be decomposed into a sum of several natural numbers that are each less than $n$. Given a natural number $n$, list all decompositions of $n$ into a sum of natural numbers, where every addend is less than $n$. In each decomposition, the numbers must be written in nondecreasing order. Then output these sequences in lexicographic order, with lexicographically smaller sequences printed first.

Input: a single natural number $n$.

Output: several addition expressions. Print one decomposition per line as $a_1+a_2+\dots+a_k$, where each $a_i$ is a natural number less than $n$, the sequence is in nondecreasing order, and the lines are sorted in lexicographic order.

Constraints: $2 \leq n \le 8$. Translated by ChatGPT 5