Arc of Dream

An Arc of Dream is a curve defined by following function:

where
a₀ = A0
a_i = a_i-1*AX+AY
b₀ = B0
b_i = b_i-1*BX+BY
What is the value of AoD(N) modulo 1,000,000,007?

There are multiple test cases. Process to the End of File.
Each test case contains 7 nonnegative integers as follows:
N
A0 AX AY
B0 BX BY
N is no more than 10¹⁸, and all the other integers are no more than 2×10⁹.

For each test case, output AoD(N) modulo 1,000,000,007.

1
1 2 3
4 5 6
2
1 2 3
4 5 6
3
1 2 3
4 5 6

4
134
1902

Zejun Wu (watashi)

2013 Multi-University Training Contest 9