Buggy python submission (verdict: Runtime Error):
from fractions import gcd
from itertools import accumulate

n, x, d = map(int, input().split())
g = gcd(x, d)
back_k = d // g
offset = x // g

min_memo = [0] + list(accumulate(range(n)))
max_memo = [0] + list(accumulate(range(n - 1, -1, -1)))

ans = 0
for k in range(n + 1):
    min_acc = min_memo[k]
    max_acc = max_memo[k]

    if k < back_k:
        ans += max_acc - min_acc + 1
        continue

    back_max = max_memo[k - back_k] - offset
    ans += max_acc - max(min_acc - 1, back_max)

print(ans)


Fixed submission:
from fractions import gcd
from itertools import accumulate

n, x, d = map(int, input().split())

if d == 0:
    if x == 0:
        print(1)
    else:
        print(n + 1)
    exit()
elif d < 0:
    x, d = -x, -d

g = gcd(x, d)
back_k = d // g
offset = x // g

lowers = [0] + list(accumulate(range(n)))
uppers = [0] + list(accumulate(range(n - 1, -1, -1)))
min_memo = [10 ** 18] * min(n + 1, back_k)
max_memo = [-(10 ** 18)] * min(n + 1, back_k)
# print(n, x, d, g, back_k, offset)
# print(lowers)
# print(uppers)

ans = 0
for k in range(n + 1):
    min_acc = lowers[k]
    max_acc = uppers[k]

    if k < back_k:
        min_memo[k] = min_acc - offset
        max_memo[k] = max_acc - offset
        ans += max_acc - min_acc + 1
        # print(k, ans, min_acc, max_acc, max_acc - min_acc + 1)
        continue

    kk = k % back_k
    back_min = min_memo[kk]
    back_max = max_memo[kk]

    if back_max < min_acc or max_acc < back_min:
        min_memo[kk] = min_acc - offset
        max_memo[kk] = max_acc - offset
        ans += max_acc - min_acc + 1
    else:
        current = max_acc - min_acc + 1
        duplicated = min(max_acc, back_max) - max(min_acc, back_min) + 1
        ans += current - duplicated
        min_memo[kk] = min(min_acc, back_min) - offset
        max_memo[kk] = max(max_acc, back_max) - offset

    # print(k, ans, min_acc, max_acc, back_min, back_max)

print(ans)

Buggy python submission (verdict: Runtime Error):
from fractions import gcd
from itertools import accumulate

n, x, d = map(int, input().split())
g = gcd(x, d)
back_k = d // g
offset = x // g

min_memo = [0] + list(accumulate(range(n)))
max_memo = [0] + list(accumulate(range(n - 1, -1, -1)))
ans = 1
# print(back_k, offset)
# print(min_memo)
# print(max_memo)

for k in range(1, n + 1):
    min_acc = min_memo[k]
    max_acc = max_memo[k]

    if k < back_k:
        ans += max_acc - min_acc + 1
        continue

    back_min = min_memo[k - back_k] - offset
    back_max = max_memo[k - back_k] - offset
    ans += max_acc - max(min_acc, back_max) + 1
    # print(ans, min_acc, max_acc, back_min, back_max)

print(ans)


Fixed submission:
from fractions import gcd
from itertools import accumulate

n, x, d = map(int, input().split())

if d == 0:
    if x == 0:
        print(1)
    else:
        print(n + 1)
    exit()
elif d < 0:
    x, d = -x, -d

g = gcd(x, d)
back_k = d // g
offset = x // g

lowers = [0] + list(accumulate(range(n)))
uppers = [0] + list(accumulate(range(n - 1, -1, -1)))
min_memo = [10 ** 18] * min(n + 1, back_k)
max_memo = [-(10 ** 18)] * min(n + 1, back_k)
# print(n, x, d, g, back_k, offset)
# print(lowers)
# print(uppers)

ans = 0
for k in range(n + 1):
    min_acc = lowers[k]
    max_acc = uppers[k]

    if k < back_k:
        min_memo[k] = min_acc - offset
        max_memo[k] = max_acc - offset
        ans += max_acc - min_acc + 1
        # print(k, ans, min_acc, max_acc, max_acc - min_acc + 1)
        continue

    kk = k % back_k
    back_min = min_memo[kk]
    back_max = max_memo[kk]

    if back_max < min_acc or max_acc < back_min:
        min_memo[kk] = min_acc - offset
        max_memo[kk] = max_acc - offset
        ans += max_acc - min_acc + 1
    else:
        current = max_acc - min_acc + 1
        duplicated = min(max_acc, back_max) - max(min_acc, back_min) + 1
        ans += current - duplicated
        min_memo[kk] = min(min_acc, back_min) - offset
        max_memo[kk] = max(max_acc, back_max) - offset

    # print(k, ans, min_acc, max_acc, back_min, back_max)

print(ans)