bee 1701 - Fibos's Sequence

Fibo is a big fan of numbers, specially of big ones. He loves sequences that grow fast, his favorite is a well known sequence, the Fibonacci Sequence. Someday he decided to create a new sequence using his favorite one. His new sequence is build multiplying consecutive Fibonacci numbers. So he gets two initial Fibonacci numbers of indexes A and B. The first element of the new sequence is the Fibonacci number of index A multiplied by the number of index B, the second one is the Fibonacci number of index A+1 multiplied by the number of index B+1, and so on. He knows how to get any element of his sequence, but he would like to know another thing. He would like to know the sum of the first N numbers of the new sequence. Can you help him?

PS: Fibonnaci(0) = 0 and Fibonnaci(1) = 1

Input

The input file has a lot of test cases. Each test case has three integers, A, B and N (1 <= A, B, N <= 1000000000), their meaning was explained in the text above. The input ends with three zeros.

Output

For each test case you have to print one number, the sum of the N first elements of Fibo's sequence. This number can be really large, so you have to print it MOD 1000000007.

Sample Input	Sample Output
1 1 5 3 4 5 0 0 0	40 438

Sample Input

Sample Output

1 1 5

3 4 5

0 0 0

438