Lighting cue stack

Simulate the cue stack of a theatre lighting console.

The rig has channels dimmer channels, numbered from 1, each at a level from 0 to 100. All start at 0, and the console starts before cue 1 (the "blackout", cue 0). cues[i] = [fade, changes] is cue i + 1: changes lists [channel, level] pairs, and fade is how many ticks the lights take to get there.

Tracking. A cue's *target* is the previous cue's target with that cue's changes applied. A channel a cue does not mention keeps whatever the cues before it set. The target of cue 0 is all zeros.

Fades. GO moves to the next cue and BACK to the previous one; either starts a fade from the levels the lights show *right now* (which may be partway through an earlier fade) to the new cue's target, over fade ticks. GO uses the fade of the cue it moves to; BACK uses the fade of the cue it leaves. A new fade replaces any fade in progress. GO on the last cue and BACK on cue 0 do nothing. A fade of 0 ticks arrives immediately.

After e ticks of a d-tick fade, a channel that started at a and is heading to b shows a + (b - a) * e / d, with the fractional part dropped toward a (never past the target; for example 33.3 becomes 33 and a decrease of 16.5 becomes 16). Once e >= d it shows b.

Commands: "WAIT n" lets n ticks pass. "SNAP" finishes the fade in progress immediately. "READ" records the current levels of all channels in order.

Input: channels, cues and commands as above.

Output: a list with one entry per READ (in order), each a list of the channels levels.