An Arc of Dream is a curve defined by following function:
where a0 = A0 ai = ai-1*AX+AY b0 = B0 bi = bi-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.