#advent of code 2020
#day 13
#kinda cheated, the chinese remainder theorem (CRT) was copy-pasted from google search results
#the source where I was reading how it works didn't really provide a good example
#will definitely look it up later :)

def gcd_extended(a, b):
    if a == 0:
        return b, 0, 1
    gcd, x1, y1 = gcd_extended(b % a, a)
    x = y1 - (b // a) * x1
    y = x1
    return gcd, x, y

def find_min_x(num, rem):
    prod = 1
    for n in num:
        prod *= n
    result = 0
    for i in range(len(num)):
        prod_i = prod // num[i]
        _, inv_i, _ = gcd_extended(prod_i, num[i])
        result += rem[i] * prod_i * inv_i
    return result % prod

PuzzleInput = open("13.in","r").read().split("\n");
timestamp = int(PuzzleInput[0]);
buses = PuzzleInput[1].split(",");f b != "x"];

times = dict();
BusList = [];
OffsetList = [];
for index, bus in enumerate(buses):
	if bus == "x": continue;
	bus = int(bus);
	BusList.append(bus);
	OffsetList.append(bus-index);
	d = timestamp%bus;
	NextStop = timestamp-d+bus;
	times[NextStop] = (bus,bus-d);

busID, WaitTime = times[min(times)];
p1 = busID * WaitTime;
p2 = find_min_x(BusList,OffsetList); #CRT
print("part 1 =",p1);
print("part 2 =",p2);