from lib import get_data, str_to_ints, mod_inverse
from math import gcd

data = get_data(__file__)
deck = list(range(10007))

# part 1
for line in data.splitlines():
    if "new stack" in line:
        deck = list(reversed(deck))
    elif "cut" in line:
        (n,) = str_to_ints(line)
        deck = deck[n:] + deck[:n]
    elif "increment" in line:
        new_deck = [-1] * len(deck)
        pos = 0
        (n,) = str_to_ints(line)
        deck = list(reversed(deck))
        while deck:
            new_deck[pos] = deck.pop()
            pos = (pos + n) % len(new_deck)
        deck = new_deck
    else:
        assert False

print(deck.index(2019))

len = 10007
orig_index = 2019

# figure out how to reverse...
index = orig_index
for line in data.splitlines():
    if "new stack" in line:
        new_index = len - (index + 1)
        rev_index = -(new_index - len + 1)
        assert rev_index == index
        index = new_index
    elif "cut" in line:
        (cut,) = str_to_ints(line)
        cut = (len + cut) % len
        if index >= cut:
            new_index = index - cut
        else:
            new_index = (len - cut) + index
        rev_index = (new_index + cut) % len
        assert rev_index == index
        index = new_index
        # calculate index from new_index and store in rev_index
    elif "increment" in line:
        (n,) = str_to_ints(line)
        assert gcd(n, len) == 1
        new_index = (n * index) % len
        m = mod_inverse(n, len)
        rev_index = (new_index * m) % len
        assert rev_index == index
        index = new_index

assert index == deck.index(2019)

# check that reverse approach works
for line in reversed(data.splitlines()):
    if "new stack" in line:
        index = -(index - len + 1)
    elif "cut" in line:
        (cut,) = str_to_ints(line)
        cut = (len + cut) % len
        index = (index + cut) % len
    elif "increment" in line:
        (n,) = str_to_ints(line)
        assert gcd(n, len) == 1
        m = mod_inverse(n, len)
        index = (index * m) % len
assert index == orig_index

lines = list(reversed(data.splitlines()))

# new length of deck
len = 119315717514047

# get expression for one loop using sympy
from sympy import symbols, simplify

index = symbols("index")
expr = index
for line in lines:
    if "new stack" in line:
        # index = -(index - len + 1)
        expr = -(expr - len + 1)
    elif "cut" in line:
        (cut,) = str_to_ints(line)
        cut = (len + cut) % len
        # index = (index + cut) % len
        expr = expr + cut
    elif "increment" in line:
        (n,) = str_to_ints(line)
        assert gcd(n, len) == 1
        m = mod_inverse(n, len)
        # index = (index * m) % len
        expr = expr * m

# we can see that expression is in the form (a - b * i) % m
expr = simplify(expr % len)
coeff_dict = expr.args[0].as_coefficients_dict()
a = coeff_dict[1]
b = -coeff_dict[index]

# math
n_shuffles = 101741582076661
r0 = 2020
m = len
p = (-b) % m
p_t = pow(p, n_shuffles, m)
inv_b1 = mod_inverse(b + 1, m)
term1 = (p_t * r0) % m
term2 = (a * (1 - p_t) * inv_b1) % m
r_t = (term1 + term2) % m
print(r_t)