Buggy python submission (verdict: Runtime Error):
def gcd(a, b):
    while b: a, b = b, a % b
    return abs(a)
N, X, D = map(int, input().split())
g = gcd(X, D)
X //= g
D //= g
if D < 0:
    X, D = -X, -D

if D == 0:
    print(N+1 if X else 1)
    exit()
E = {}
for i in range(N+1):
    k = i % D
    l, r = i * (2*X+(i-1)*D) // 2, i * (2*X+(2*N-i-1)*D) // 2
    c = (r - l) // D + 1 if D else 1
    if k not in E:
        E[k] = (l, r, c)
    else:
        ll, rr, cc = E[k]
        if r < ll:
            E[k] = (l, rr, cc + c)
        elif l > rr:
            E[k] = (ll, r, cc + c)
        elif l < ll:
            E[k] = (l, rr, cc + ((ll - l) // D if D else 1))
        elif r > rr:
            E[k] = (ll, r, cc + ((r - rr) // D if D else 1))

ans = 0
for e in E:
    l, r, c = E[e]
    ans += c

print(ans)


Fixed submission:
def gcd(a, b):
    while b: a, b = b, a % b
    return abs(a)
N, X, D = map(int, input().split())
if D == 0:
    print(N+1 if X else 1)
    exit()
g = gcd(X, D)
X //= g
D //= g
if D < 0:
    X, D = -X, -D

E = {}
for i in range(N+1):
    k = i % D
    l, r = i * (2*X+(i-1)*D) // 2, i * (2*X+(2*N-i-1)*D) // 2
    c = (r - l) // D + 1 if D else 1
    if k not in E:
        E[k] = (l, r, c)
    else:
        ll, rr, cc = E[k]
        if r < ll:
            E[k] = (l, rr, cc + c)
        elif l > rr:
            E[k] = (ll, r, cc + c)
        elif l < ll:
            E[k] = (l, rr, cc + ((ll - l) // D if D else 1))
        elif r > rr:
            E[k] = (ll, r, cc + ((r - rr) // D if D else 1))

ans = 0
for e in E:
    l, r, c = E[e]
    ans += c

print(ans)

Buggy python submission (verdict: Runtime Error):
def gcd(a, b):
    while b: a, b = b, a % b
    return abs(a)
N, X, D = map(int, input().split())
g = gcd(X, D)
X //= g
D //= g
if D < 0:
    X, D = -X, -D

E = {}
for i in range(N+1):
    k = i % D
    l, r = i * (2*X+(i-1)*D) // 2, i * (2*X+(2*N-i-1)*D) // 2
    c = (r - l) // D + 1 if D else 1
    if k not in E:
        E[k] = (l, r, c)
    else:
        ll, rr, cc = E[k]
        if r < ll:
            E[k] = (l, rr, cc + c)
        elif l > rr:
            E[k] = (ll, r, cc + c)
        elif l < ll:
            E[k] = (l, rr, cc + ((ll - l) // D if D else 1))
        elif r > rr:
            E[k] = (ll, r, cc + ((r - rr) // D if D else 1))

ans = 0
for e in E:
    l, r, c = E[e]
    ans += c

print(ans)


Fixed submission:
def gcd(a, b):
    while b: a, b = b, a % b
    return abs(a)
N, X, D = map(int, input().split())
if D == 0:
    print(N+1 if X else 1)
    exit()
g = gcd(X, D)
X //= g
D //= g
if D < 0:
    X, D = -X, -D

E = {}
for i in range(N+1):
    k = i % D
    l, r = i * (2*X+(i-1)*D) // 2, i * (2*X+(2*N-i-1)*D) // 2
    c = (r - l) // D + 1 if D else 1
    if k not in E:
        E[k] = (l, r, c)
    else:
        ll, rr, cc = E[k]
        if r < ll:
            E[k] = (l, rr, cc + c)
        elif l > rr:
            E[k] = (ll, r, cc + c)
        elif l < ll:
            E[k] = (l, rr, cc + ((ll - l) // D if D else 1))
        elif r > rr:
            E[k] = (ll, r, cc + ((r - rr) // D if D else 1))

ans = 0
for e in E:
    l, r, c = E[e]
    ans += c

print(ans)

Buggy python submission (verdict: Runtime Error):
def gcd(a, b):
    while b: a, b = b, a % b
    return abs(a)
N, X, D = map(int, input().split())
g = gcd(X, D)
X //= g
D //= g
if D < 0:
    X, D = -X, -D

E = {}
for i in range(N+1):
    k = i % D
    l, r = i * (2*X+(i-1)*D) // 2, i * (2*X+(2*N-i-1)*D) // 2
    c = (r - l) // D + 1
    if k not in E:
        E[k] = (l, r, c)
    else:
        ll, rr, cc = E[k]
        if r < ll:
            E[k] = (l, rr, cc + c)
        elif l > rr:
            E[k] = (ll, r, cc + c)
        elif l < ll:
            E[k] = (l, rr, cc + (ll - l) // D)
        elif r > rr:
            E[k] = (ll, r, cc + (r - rr) // D)

ans = 0
for e in E:
    l, r, c = E[e]
    ans += c

print(ans)

Fixed submission:
def gcd(a, b):
    while b: a, b = b, a % b
    return abs(a)
N, X, D = map(int, input().split())
if D == 0:
    print(N+1 if X else 1)
    exit()
g = gcd(X, D)
X //= g
D //= g
if D < 0:
    X, D = -X, -D

E = {}
for i in range(N+1):
    k = i % D
    l, r = i * (2*X+(i-1)*D) // 2, i * (2*X+(2*N-i-1)*D) // 2
    c = (r - l) // D + 1 if D else 1
    if k not in E:
        E[k] = (l, r, c)
    else:
        ll, rr, cc = E[k]
        if r < ll:
            E[k] = (l, rr, cc + c)
        elif l > rr:
            E[k] = (ll, r, cc + c)
        elif l < ll:
            E[k] = (l, rr, cc + ((ll - l) // D if D else 1))
        elif r > rr:
            E[k] = (ll, r, cc + ((r - rr) // D if D else 1))

ans = 0
for e in E:
    l, r, c = E[e]
    ans += c

print(ans)