Problem:
Score : 600 points

Problem Statement

We have an integer sequence A of length N, where A_1 = X, A_{i+1} = A_i + D (1 \leq i < N ) holds.

Takahashi will take some (possibly all or none) of the elements in this sequence, and Aoki will take all of the others.

Let S and T be the sum of the numbers taken by Takahashi and Aoki, respectively. How many possible values of S - T are there?

Constraints

-10^8 \leq X, D \leq 10^8

1 \leq N \leq 2 \times 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N X D

Output

Print the number of possible values of S - T.

Sample Input 1

3 4 2

Sample Output 1

8

A is (4, 6, 8).

There are eight ways for (Takahashi, Aoki) to take the elements: ((), (4, 6, 8)), ((4), (6, 8)), ((6), (4, 8)), ((8), (4, 6))), ((4, 6), (8))), ((4, 8), (6))), ((6, 8), (4))), and ((4, 6, 8), ()).

The values of S - T in these ways are -18, -10, -6, -2, 2, 6, 10, and 18, respectively, so there are eight possible values of S - T.

Sample Input 2

2 3 -3

Sample Output 2

2

A is (3, 0). There are two possible values of S - T: -3 and 3.

Sample Input 3

100 14 20

Sample Output 3

49805

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

from operator import itemgetter

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

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

p = dict()
q = dict()

for k in range(n+1):
    temp = k * x % d
    if temp in p.keys():
        #print((k - p[temp]) * x)
        a = (k - p[temp]) * x // d
        L = (k-1)*k//2 + a
        H = (2*n-k-1)*k//2 + a
        q[temp].append([L, H])
    else:
        p[temp] = k
        L = (k-1)*k//2
        H = (2*n-k-1)*k//2
        q[temp] = [[L, H]]

#print(q)
ans = 0

for z in q.values():
    c = - float('inf')
    #print(sorted(z))
    for a, b in sorted(z):
        if a > c:
            ans += b - a + 1
        elif b > c:
            ans += b - c
        c = b
        #print(ans, a, b)

print(ans)