Revenge of GCD

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)


In mathematics, the greatest common divisor (gcd), also known as the greatest common factor (gcf), highest common factor (hcf), or greatest common measure (gcm), of two or more integers (when at least one of them is not zero), is the largest positive integer that divides the numbers without a remainder.

Today, GCD takes revenge on you. You have to figure out the k-th GCD of X and Y.


The first line contains a single integer T, indicating the number of test cases.

Each test case only contains three integers X, Y and K.

[Technical Specification]
1. 1 <= T <= 100
2. 1 <= X, Y, K <= 1 000 000 000 000


For each test case, output the k-th GCD of X and Y. If no such integer exists, output -1.

Sample Input

3 2 3 1 2 3 2 8 16 3

Sample Output

1 -1 2




BestCoder Round #10