#!/usr/bin/env ruby

require "debug"
require "matrix"

input = (ARGV.first.nil? ? DATA : ARGF)
  .read
  .scan(/(\d+)/m)
  .each_slice(6)
  .to_a
  .map { _1.flatten.map(&:to_i).each_slice(2).to_a }
  .map { [:a, :b, :prize].zip(_1).to_h }

def solve(input, offset = 0)
  input.map do |machine|
    a = Matrix.columns([ # why does rotating matrix work?
      [machine[:a].first, machine[:a].last],
      [machine[:b].first, machine[:b].last]
    ])
    b = Matrix[
      [machine[:prize].first + offset],
      [machine[:prize].last + offset]
    ]

    (a.inverse * b).to_a.flatten
  end
    .select { _1.denominator == 1 && _2.denominator == 1 }
    .map { 3 * _1 + _2 }
    .sum
end

p solve(input).to_i
p solve(input, 10_000_000_000_000).to_i

__END__
Button A: X+94, Y+34
Button B: X+22, Y+67
Prize: X=8400, Y=5400

Button A: X+26, Y+66
Button B: X+67, Y+21
Prize: X=12748, Y=12176

Button A: X+17, Y+86
Button B: X+84, Y+37
Prize: X=7870, Y=6450

Button A: X+69, Y+23
Button B: X+27, Y+71
Prize: X=18641, Y=10279