A board game rolls dice dice one after another; each die shows a number from 1 to faces. Return
every ordered sequence of rolls whose total is exactly target. [1, 4] and [4, 1] are
different sequences. The sequences may be returned in any order.
Examples
Input: dice = 2, faces = 4, target = 5
Output: [[1, 4], [2, 3], [3, 2], [4, 1]]
Input: dice = 3, faces = 6, target = 2
Output: []
Explanation: three dice always show at least 3.
Input: dice = 1, faces = 6, target = 6
Output: [[6]]
Constraints
0 <= dice <= 5,1 <= faces <= 8,0 <= target <= 40
Goals
- Generate ordered sequences where every level has the same set of choices
- Prune a branch when the remaining sum is out of reach