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)

import queue
import math
import copy
"""
N = int(input())
#S = input()
# (N,M) = (int(i) for i in input().split(" "))
# A = [int(i) for i in input().split()]
A = []
for i in range(N):
	A.append(int(input()))

print(A)

"""

(N,X,D) = (int(i) for i in input().split(" "))
mp = {}
if D == 0:
	if X == 0:
		ans = 0
	else:
		ans = N+1
else:
	for i in range(N+1):
		md = (i*X)%D
		if not md in mp:
			mp[md] = []
		k = 0
		for j in range(i):
			k += j
		mp[md].append([k+((i*X)-md)//D,0])
		k = 0
		for j in range(i):
			k += N-j-1
		mp[md].append([k+((i*X)-md)//D+1,1])
	#print(mp)
	ans = 0
	for k in mp.keys():
		s = sorted(mp[k])
		#print(s)
		md = 0
		bef = 0
		for t in s:
			if md > 0:
				ans += t[0] - bef
			bef = t[0]
			if t[1] == 0:
				md += 1
			else:
				md -= 1
print(ans)