# Practice on Toph

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## GCD and NOD

Given 3 numbers, G, A and B we have to find two numbers M and N such that they satisfy the following conditions:

- M and N have no other prime divisor except 2 and 3
- Greatest common divisor of M and N is G
- Number of divisor of M is A
- Number of divisor of N is B
- M is between 1 and 10
^{18} - N is between 1 and 10
^{18}

It is possible that multiple pairs of M and N satisfy the above conditions. In such a case, we want to find the pair where M is minimum. If there is still tie, then we minimize N.

It is guaranteed that a solution always exists.

#### Input

The first line contains a single integer T (T ≤ 100) denoting number of test case. The next T lines describes each test case. Each test case is a single line containing three integers: G, A and B.

#### Output

For each test case, output a single line containing two integers: M and N satisfying the conditions mentioned in problem statement above.

#### Samples

Input | Output |
---|---|

2 1 2 2 6 6 8 | 2 3 12 54 |

#### forthright48

Samiul is a student at North South University and a part-time Software Engineer at Mukto Software Ltd. Sport programming is one of his hobbies. He loves reading manga - One Piece being his favorite. →