TV Remote Tuner

Track the channel a TV is tuned to while someone uses its remote control.

The TV receives the channels listed in channels (increasing order). It starts on channels[0] and has no previous channel yet. The remote has the digit buttons "0"-"9", "UP", "DOWN" and "LAST". presses is a list of [time, button] pairs in non-decreasing time order.

Digit entry. Digits typed one after another build an *entry*, up to 3 digits. An entry is committed when one of these happens, whichever comes first:

• it reaches 3 digits (immediately);
• another button is pressed at a time at least wait after the entry's last digit was pressed. The entry is committed first, and then that button is handled as usual (a digit starts a new entry, so two digits wait or more apart never join);
• a non-digit button is pressed (the entry is committed first, then the button works);
• the presses run out (the entry is committed).

Committing an entry reads it as a number ("007" is 7). If a channel with that number exists, the TV tunes to it. Otherwise the entry is thrown away and nothing changes. Tuning to the channel you are already on changes nothing, including the previous channel.

Other buttons. UP tunes to the next higher channel in the list and DOWN to the next lower one; both wrap around between the highest and the lowest. LAST swaps the current channel with the previous one, and does nothing if there is no previous channel. Whenever the TV changes channel, the channel it left becomes the previous channel.

Input: channels, wait, presses.

Output: the list of channels the TV was tuned to, in order, starting with the initial channel and adding a channel each time the TV actually changes to a different one.