require_relative 'util'

# --- Day 15: Timing is Everything ---

# The halls open into an interior plaza containing a large kinetic
# sculpture. The sculpture is in a sealed enclosure and seems to
# involve a set of identical spherical capsules that are carried to
# the top and allowed to bounce through the maze of spinning pieces.

# Part of the sculpture is even interactive! When a button is pressed,
# a capsule is dropped and tries to fall through slots in a set of
# rotating discs to finally go through a little hole at the bottom and
# come out of the sculpture. If any of the slots aren't aligned with
# the capsule as it passes, the capsule bounces off the disc and soars
# away. You feel compelled to get one of those capsules.

# The discs pause their motion each second and come in different
# sizes; they seem to each have a fixed number of positions at which
# they stop. You decide to call the position with the slot 0, and
# count up for each position it reaches next.

# Furthermore, the discs are spaced out so that after you push the
# button, one second elapses before the first disc is reached, and one
# second elapses as the capsule passes from one disc to the one below
# it. So, if you push the button at time=100, then the capsule reaches
# the top disc at time=101, the second disc at time=102, the third
# disc at time=103, and so on.

# The button will only drop a capsule at an integer time - no
# fractional seconds allowed.

# For example, at time=0, suppose you see the following arrangement:

# - Disc #1 has 5 positions; at time=0, it is at position 4.
# - Disc #2 has 2 positions; at time=0, it is at position 1.

# If you press the button exactly at time=0, the capsule would start
# to fall; it would reach the first disc at time=1. Since the first
# disc was at position 4 at time=0, by time=1 it has ticked one
# position forward. As a five-position disc, the next position is 0,
# and the capsule falls through the slot.

# Then, at time=2, the capsule reaches the second disc. The second
# disc has ticked forward two positions at this point: it started at
# position 1, then continued to position 0, and finally ended up at
# position 1 again. Because there's only a slot at position 0, the
# capsule bounces away.

# If, however, you wait until time=5 to push the button, then when the
# capsule reaches each disc, the first disc will have ticked forward
# 5+1 = 6 times (to position 0), and the second disc will have ticked
# forward 5+2 = 7 times (also to position 0). In this case, the
# capsule would fall through the discs and come out of the machine.

# However, your situation has more than two discs; you've noted their
# positions in your puzzle input. What is the first time you can press
# the button to get a capsule?