
Score : 600 points
Problem StatementWe 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.
InputInput is given from Standard Input in the following format:
N X D
OutputPrint the number of possible values of S - T.
Sample Input 13 4 2
Sample Output 18
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 22 3 -3
Sample Output 22
A is (3, 0). There are two possible values of S - T: -3 and 3.
Sample Input 3100 14 20
Sample Output 349805
