9967: ABC315 —— G - Ai + Bj + Ck = X (1 <= i, j, k <= N)
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Description
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.
- $1 \le i,j,k \le N$
- $Ai+Bj+Ck=X$
- $1 \le i,j,k \le N$
- $Ai+Bj+Ck=X$
Input
The input is given from Standard Input in the following format:
```
$N$ $A$ $B$ $C$ $X$
```
```
$N$ $A$ $B$ $C$ $X$
```
Output
Print the answer as an integer.
Constraints
- All input values are integers.
- $1 \le N \le 10^6$
- $1 \le A,B,C \le 10^9$
- $1 \le X \le 3 \times 10^{15}$
- $1 \le N \le 10^6$
- $1 \le A,B,C \le 10^9$
- $1 \le X \le 3 \times 10^{15}$
Sample 1 Input
5 3 1 5 15
Sample 1 Output
3
The following three triples satisfy the conditions.
- (1,2,2) : 3×1+1×2+5×2=15
- (2,4,1) : 3×2+1×4+5×1=15
- (3,1,1) : 3×3+1×1+5×1=15
Sample 2 Input
1 1 1 1 1
Sample 2 Output
0
Sample 3 Input
100000 31415 92653 58979 1000000000
Sample 3 Output
2896