Preparing NOJ

Product Oriented Recurrence

1000ms 262144K

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:

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, $$$f_{17} \approx 2.28 \times 10^{29587}$$$.

Info

CodeForces

Provider CodeForces

Origin Codeforces Round #566 (Div. 2)

Code CF1182E

Tags

dpmathmatricesnumber theory

Submitted 23

Passed 13

AC Rate 56.52%

Date 07/21/2019 13:42:54

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