Score : $550$ points

## 问题描述

给定整数 $N,A,B,C,X$。求满足以下所有条件的整数三元组 $(i,j,k)$ 的数量。

-   $1 \le i,j,k \le N$
-   $Ai + Bj + Ck = X$

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given integers $N,A,B,C,X$. Find the number of triples of integers $(i,j,k)$ that satisfy all of the following conditions.

• $1 \le i,j,k \le N$
• $Ai+Bj+Ck=X$

Constraints

• All input values are integers.
• $1 \le N \le 10^6$
• $1 \le A,B,C \le 10^9$
• $1 \le X \le 3 \times 10^{15}$

Input

The input is given from Standard Input in the following format:

$N$ $A$ $B$ $C$ $X$

Output

Print the answer as an integer.

Sample Input 1

5 3 1 5 15

Sample Output 1

3

The following three triples satisfy the conditions.

• $(1,2,2)$ : $3 \times 1 + 1 \times 2 + 5 \times 2 = 15$
• $(2,4,1)$ : $3 \times 2 + 1 \times 4 + 5 \times 1 = 15$
• $(3,1,1)$ : $3 \times 3 + 1 \times 1 + 5 \times 1 = 15$

Sample Input 2

1 1 1 1 1

Sample Output 2

0

Sample Input 3

100000 31415 92653 58979 1000000000

Sample Output 3

2896

update @ 2024/3/10 09:01:18