#P1182E. Product Oriented Recurrence
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ID: 4418
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: 8
Uploaded By:
Hydro
Tags> 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 $f_{n} \bmod (10^{9} + 7)$.
5 1 2 5 3
17 97 41 37 11
72900
317451037
Note
In the first example, $f_{4} = 90$, $f_{5} = 72900$.
In the second example, $f_{17} \approx 2.28 \times 10^{29587}$.