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Find the term
Tag(s):

Hard, Math

Problem
Editorial
Analytics

The $$ n^{th}$$ term of a mathematical series is described as follows:

$$ K_{n} = K_{n-1} - K_{n+1}$$

You have to find the $$m^{th}$$ term, given the first two terms $$K_{1}$$ and $$K_{2}$$ of the series.

Input format:
The first line contains T, which denotes the number of test cases, after which T test cases follow.
Each test case is made up of two lines. The first line contains $$K_{1}$$ and $$K_{2}$$, the first two terms of the series. The second line contains m, for which $$K_{m}$$ has to be calculated.

Output format:
T lines each containing the value of $$K_{m}$$ for the corresponding test case. Since the value of $$K_{m}$$ can be large, print the value modulo $$10^9 +7$$.

Input constraints:
$$1 \leq T \leq 10^5$$
$$1 \leq N \leq 2 \times 10^9$$
$$|K_1| \leq 10^9$$
$$|K_2| \leq 10^9$$

SAMPLE INPUT
2
4 2
3
6 7
2
SAMPLE OUTPUT
2
7
Explanation

In Test case 1:

$$K_3 = K_1 - K_2 = 4 - 2 = 2$$

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Scala 2.11.8, Swift, Visual Basic

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