All Combinations of K Numbers

Return every way to choose k numbers from 1, 2, ..., n, each written in increasing order, listed in dictionary order. For n = 4 and k = 2: [1,2], [1,3], [1,4], [2,3], [2,4], [3,4].

Examples

Example 1

Input:

all_combinations(4, 2)

Output:

[[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]

Example 2

Input:

all_combinations(1, 1)

Output:

[[1]]

Constraints

• 1 <= n <= 20
• 0 <= k <= n
• The answer has at most C(n, k) lists; the tests keep it under 200,000.