Bob and Alice decided that problem $X$ needs at least $N$ distinct solutions to be written. It does not matter how many solutions each of them will write, they need to write at least $N$ solutions in total.

Bob needs $t_1$ units of time to write a solution, and Alice needs $t_2$ units of time. They start to work simultaneously at time $0$. For example, Bob finishes writing his first solution at time $t_1$, his second solution at $2*t_1$, and so on.

Bob and Alice are working using the same algorithm. Each time Bob or Alice finishes writing a solution, he checks on how many solutions have already been written up to the current time moment $t$. If the number of such solutions is strictly less than $N$, then he starts writing the next solution. If a member began working on a problem, he does not stop working under any circumstances and he will surely finish it.

Bob and Alice realize that if they act on this algorithm, they will not necessarily write exactly $N$ solutions in total. 

Considering that Bob and Alice work non-stop, find how many solutions they wrote in total and the moment when the latest solution was finished. 

Input format

• The first line contains an integer $T$ denoting the number of test cases.
• The first line of each test case contains three space-separated integers $N$, $t_1$ and $t_2$.

Output format

For each test case, print two integers $m$ and $f$, where $m$ is the number of written solutions and $f$ is the moment when the last solution was finished. Output for each test case should be in a new line.

Constraints

$1 \le T \le 100000\\ 1 \le N,t_1,t_2 \le 1000000000$