Combinations with Repetition

Problem

Given two natural numbers n and m, write a solution function that returns all sets of m numbers selected from the integers between 1 and n that satisfy the following conditions:

Conditions:

• Each set contains exactly $A_1, A_2, \cdots, A_m$ numbers.
• $1 \leq A_1 \leq A_2 \leq \cdots \leq A_m \leq n$.
• If multiple sets satisfy the above conditions, return the sets in lexicographical order.

Constraints

• n is a natural number less than or equal to 12.
• m is a natural number less than or equal to 12.

Test Case

Explanation for Test Case 1

• From the integers 1, 2, and 3, selecting and arranging 2 numbers with repetition allowed and in non-decreasing order produces the following sets: [1,1], [1,2], [1,3], [2,2], [2,3], [3,3].
• Sorting these sets lexicographically results in [[1,1],[1,2],[1,3],[2,2],[2,3],[3,3]].

Explanation for Test Case 2

• From the integers 1, 2, 3, 4, and 5, selecting and arranging 1 number with repetition allowed and in non-decreasing order produces the following sets: [1], [2], [3], [4], [5].
• Sorting these sets lexicographically results in [[1],[2],[3],[4],[5]].

Explanation for Test Case 3

• From the integers 1 and 2, selecting and arranging 3 numbers with repetition allowed and in non-decreasing order produces the following sets: [1,1,1], [1,1,2], [1,2,2], [2,2,2].
• Sorting these sets lexicographically results in [[1,1,1],[1,1,2],[1,2,2],[2,2,2]].