Product Oriented Recurrence
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 $f_{n} \bmod (10^{9}+7)$.
The only line contains five integers $n$, $f_{1}$, $f_{2}$, $f_{3}$, and $c$ ($4 \le n \le 10^{18}$, $1 \le f_{1}$, $f_{2}$, $f_{3}$, $c \le 10^{9}$).
Print $f_{n} \bmod (10^{9} + 7)$.
Input
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
Print $f_{n} \bmod (10^{9} + 7)$.
Samples
5 1 2 5 3
72900
17 97 41 37 11
317451037
Note
In the first example, $f_{4} = 90$, $f_{5} = 72900$.
In the second example, $f_{17} \approx 2.28 \times 10^{29587}$.