An Arc of Dream is a curve defined by following function:
where
a 0 = A0
a i = a i-1*AX+AY
b 0 = B0
b i = b i-1*BX+BY
What is the value of AoD(N) modulo 1,000,000,007?
Input
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 10 18, and all the other integers are no more than 2×10 9.
Output
For each test case, output AoD(N) modulo 1,000,000,007.
Sample Input
1 1 2 3 4 5 6 2 1 2 3 4 5 6 3 1 2 3 4 5 6
Sample Output
4 134 1902
怎么构造？
根据这些已知条件：
A(n)=A(n-1)+ai-1bi-1
ai*bi=ai-1*bi-1*AX*BX+ai-1*AX*BY+bi-1*AY*BX+AY*BY
a i = a i-1*AX+AY
b i = b i-1*BX+BY
A（n）=A(n-1)+ai*bi
构造矩阵：