Codeforces Round 566 (Div. 2) |
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Finished |

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dp

math

matrices

number theory

*2300

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E. Product Oriented Recurrence

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet $$$f_{x} = c^{2x-6} \cdot f_{x-1} \cdot f_{x-2} \cdot f_{x-3}$$$ 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 $$$f_{n} \bmod (10^{9} + 7)$$$.

Examples

Input

5 1 2 5 3

Output

72900

Input

17 97 41 37 11

Output

317451037

Note

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

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

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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