Combinations

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.
• $1 \leq A_1 < A_2 < \cdots < A_m \leq n$.
• If multiple sets satisfy the above conditions, return the sets in lexicographical order.

Constraints

• n is a natural number less than or equal to 15.
• m is a natural number less than or equal to n.

Test Case

Explanation for Test Case 1

• From the integers 1, 2, and 3, selecting and arranging 2 numbers in ascending order produces the following 3 sets: [1,2], [1,3], [2,3].
• Sorting these sets lexicographically results in [[1,2],[1,3],[2,3]].

Explanation for Test Case 2

• From the integers 1, 2, 3, 4, and 5, selecting and arranging 1 number in ascending order produces the following 5 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, 2, 3, 4, and 5, selecting and arranging all 5 numbers in ascending order produces a single set: [1,2,3,4,5].
• Sorting these sets lexicographically results in [[1,2,3,4,5]].