Product Oriented Recurrence

Description:

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 $$$f_{n} \bmod (10^{9} + 7)$$$.

Sample Input:

5 1 2 5 3

Sample Output:

72900

Sample Input:

17 97 41 37 11

Sample Output:

317451037

Note:

In the first example, $$$f_{4} = 90$$$, $$$f_{5} = 72900$$$.

In the second example, $$$f_{17} \approx 2.28 \times 10^{29587}$$$.