Painting Houses

You own a company that hires painters to paint houses. You can hire as many painters as you want. For each painter you hire, you pay X dollars, no matter how long that painter works on the house. You also pay a penalty of $D \times P$ dollars if it takes $D$ days to finish painting the house. This penalty does not depend on the number of painters. Even if the time is not a whole number of days, you are penalized only for the exact time taken. All painters paint at the same rate. One painter finishes the house in $K$ days. $M$ painters cooperate so well that they finish in $K/M$ days. Find the minimum total cost, including the payment to the painters and the penalty, to get the house painted.

The first line contains a single integer $n$, the number of data sets. Each of the following data sets is one line with three space-separated integers $K$, $P$, and $X$ ($1 \le K, P, X \le 10000$).

For each data set, print on a single line the minimum cost, rounded and displayed to exactly three decimal places.