An Orz panda find a very interesting problem. His problem is that x + y = A, x * y = B, where A and B are constant, how to calculate x² + y², x³ + y³ , …… xⁿ + yⁿ . Panda wants you to help him solve it. If you can solve it successfully, he’ll summon many small pandas to Orz you.
In this problem, you just need calculate the result of xn + yn . Since the result can be very large, determine the remainder after dividing it by 1000000007.

There several test cases,  process to EOF,  about 200 test cases.
For each test case, one line contains three A, B, n.
0 ≤ A,  B ≤ 1000000,  1 ≤ n ≤ 10000.

Print a single integer modulo1000000007.