Immortal Rabbits

In a parallel world, a human called Fibonacci was playing with his computer. Suddenly, he got a BSoD (The Blue Screen of Death). While his OS restarted, he realized that a group of immortal rabbits grows as shown: 0, 1, 1, 2, 3, 5, 8, 13, 21, ... , where each number is the number of pairs that were alive each month, and because of their immortality, the series could get really big in a short period of time. In other words, the number of pairs of those rabbits is the sum of the pairs of the previous two months. More formally:  0 if n=0 fn=1 if n=1 fn−1+fn−2 if n≥1 Trying to make a general statement, Fibonacci changed the root values (0 and 1) to variables A and B,sof0 =Aandf1 =B. When the computer was finally ready, and his IDE loaded, he decided to make a program with the cool Java’s BigInteger-class to calculate how many rabbits will exist in the month m. After coding the algorithm he realized it wasn’t as fast as he expected, so he decided to send telepathic messages to people from other dimensions asking for a fast algorithm of big numbers to solve this problem. Our problemsetters at RPC got that message so they want to commend you that non-trivial task! Input The input starts with a line that contains an integer T ≤ 1000 that represents the number of calculations that Fibonacci wants to do. The following T lines will contain 3 integers A, B, m (0 ≤ A, B ≤ 1000000, 0 ≤ m ≤ 100000). Output For each test case print the number of rabbits in the month m with an end of line. Sample Input 1 100 100 50 Sample Output 2036501107400