from functools import reduce


test = (
	939,
	"7,13,x,x,59,x,31,19",
)

data = (
	1002462,
	"37,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,41,x,x,x,x,x,x,x,x,x,601,x,x,x,x,x,x,x,x,x,x,x,19,x,x,x,x,17,x,x,x,x,x,23,x,x,x,x,x,29,x,443,x,x,x,x,x,x,x,x,x,x,x,x,13",
)


def part1(departure, bus_ids):
	buses = [int(x) for x in bus_ids.split(",") if x != "x"]
	distances = [(departure // x + 1) * x - departure for x in buses]
	idx = distances.index(min(distances))
	return buses[idx], distances[idx]


def part2(bus_ids):
	# t = bus_id % bus_id - idx
	buses = [int(0 if x == "x" else x) for x in bus_ids.split(",")]
	p = [x - buses.index(x) for x in buses if x != 0]
	n = [x for x in buses if x != 0]
	cr = chinese_remainder(n, p)
	return cr


def chinese_remainder(n, p):
	prod = reduce(lambda a,b: a*b, n)

	sum = 0
	for div, rem in zip(n, p):
		pp = prod // div
		i = pow(pp, -1, div)
		sum += rem * pp * i

	return sum % prod


id, wait = part1(*test)
assert id*wait == 295

id, wait = part1(*data)
print(f"1: Answer is {id*wait}")

assert chinese_remainder([3, 5, 7], [2, 3, 2]) == 23

assert part2(test[1]) == 1068781
assert part2("17,x,13,19") == 3417
assert part2("67,7,59,61") == 754018
assert part2("67,x,7,59,61") == 779210
assert part2("67,7,x,59,61") == 1261476
assert part2("1789,37,47,1889") == 1202161486

ts = part2(data[1])
print(f"2: Answer is {ts}")