Domino Chain Toppling

Push some dominoes along a table and report which ones end up lying down.

Domino i stands at positions[i] (strictly increasing) and is heights[i] tall. Time moves in whole ticks.

• When a domino falls at tick t toward higher positions (right), it strikes every domino j with positions[i] < positions[j] <= positions[i] + heights[i]; domino j is struck at tick t + (positions[j] - positions[i]). Falling toward lower positions (left) is symmetric: it strikes every j with positions[i] - heights[i] <= positions[j] < positions[i], at tick t + (positions[i] - positions[j]). The reach is the whole height, so a tall domino can strike dominoes beyond a shorter neighbour directly.
• A standing domino that is struck falls at that very tick, in the direction it was struck: a domino struck by one falling right falls right, and one struck by one falling left falls left. If a domino receives strikes from both directions at the same tick, it falls right.
• A domino that is already down ignores everything, including strikes that were scheduled before it fell.
• pushes is a list of [tick, index, direction] where direction is "R" or "L". A push acts exactly like a strike from that direction at that tick on domino index (so it can tie with other strikes). A push on a domino that is already down at that tick does nothing.

Input: positions, heights, pushes.

Output: [fallen, last_tick, standing]: how many dominoes fell, the tick at which the last one fell (0 if none fell), and the sorted indices of the dominoes still standing.