github.com/captn3m0/codechef.git

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---
<span class="solution-visible-txt">All submissions for this problem are available.</span><h3>Read problems statements in <a href="http://www.codechef.com/download/translated/AUG18/hindi/GCDMOD.pdf" target="_blank">Hindi,</a>
<a href="http://www.codechef.com/download/translated/AUG18/mandarin/GCDMOD.pdf" target="_blank">Mandarin chinese</a>
, <a href="http://www.codechef.com/download/translated/AUG18/russian/GCDMOD.pdf" target="_blank">Russian</a> and <a href="http://www.codechef.com/download/translated/AUG18/vietnamese/GCDMOD.pdf" target="_blank">Vietnamese</a> as well.</h3>

At ShareChat, there are are plenty of interesting problems to solve. Here is one of them.

Given integers $A$, $B$ and $N$, you should calculate the [GCD](https://en.wikipedia.org/wiki/Greatest_common_divisor) of $A^N + B^N$ and $|A - B|$. (Assume that $GCD(0, a) = a$ for any positive integer $a$). Since this number could be very large, compute it modulo $1000000007$ ($10^9 + 7$).

### Input
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains three space-separated integers $A$, $B$ and $N$.

### Output
For each test case, print a single line containing one integer — the required GCD modulo $10^9 + 7$.

### Constraints
- $1 \le T \le 10$
- $1 \le A, B, N \le 10^{12}$
- $B \le A$

### Subtasks
**Subtask #1 (10 points):** $1 \le A, B, N \le 10$

**Subtask #2 (40 points):** $1 \le A, B, N \le 10^9$

**Subtask #3 (50 points):** original constraints

### Example Input
```
2
10 1 1
9 1 5
```

### Example Output
```
1
2
```

### Explanation
**Example case 1:** $GCD(10^1 + 1^1, 10 - 1) = GCD(11, 9) = 1$

**Example case 2:** $GCD(9^5 + 1^5, 9 - 1) = GCD(59050, 8) = 2$