Sum Difference

AtCoder

IDabc147_f

Time2000ms

Memory256MB

Difficulty—

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: $N$ $X$ $D$ [samples]

Samples

Input #1

3 4 2

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 $S - T$.

Input #2

2 3 -3

Output #2

2

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

Input #3

100 14 20

Output #3

API Response (JSON)

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    "name": "Sum Difference",
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      "content": "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",
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      "statement_type": "Markdown",
      "content": "We have an integer sequence $A$ of length $N$, where $A_1 = X, A_{i+1} = A_i + D (1 \\leq i < N )$ holds.\nTakahashi will take some (possibly all or none) of the elements in this sequence, and Aoki will...",
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