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: Time Limit Exceeded)

n, x, d = map(int, input().split())
if d == 0:
  if x == 0:
    print(1)
    quit()
  else:
    print(n + 1)
    quit()
if d < 0:
  x, d = -x, -d
lst = []
dic = {0: [0]}
for k in range(1, n + 1):
    left = (k - 1) * k // 2
    right = (2 * n - k - 1) * k // 2
    tmplst = [k * x + i * d for i in range(left, right + 1)]
    mod = k * x % d
    if mod in dic:
      dic[mod].extend(tmplst)
    else:
      dic[mod] = tmplst
c = 0
for i in dic.values():
  c += len(set(i))
print(c)