Description:
Let $$$f_{x} = c^{2x-6} \cdot f_{x-1} \cdot f_{x-2} \cdot f_{x-3}$$$ for $$$x \ge 4$$$.
You have given integers $$$n$$$, $$$f_{1}$$$, $$$f_{2}$$$, $$$f_{3}$$$, and $$$c$$$. Find $$$f_{n} \bmod (10^{9}+7)$$$.
Input Format:
The only line contains five integers $$$n$$$, $$$f_{1}$$$, $$$f_{2}$$$, $$$f_{3}$$$, and $$$c$$$ ($$$4 \le n \le 10^{18}$$$, $$$1 \le f_{1}$$$, $$$f_{2}$$$, $$$f_{3}$$$, $$$c \le 10^{9}$$$).
Output Format:
Print $$$f_{n} \bmod (10^{9} + 7)$$$.
Note:
In the first example, $$$f_{4} = 90$$$, $$$f_{5} = 72900$$$.
In the second example, $$$f_{17} \approx 2.28 \times 10^{29587}$$$.