Special Shop - HackerEarth Problem Solution

Creatnx now wants to decorate his house by flower pots. He plans to buy exactly $N$ ones. He can only buy them from Triracle's shop. There are only two kind of flower pots available in that shop. The shop is very strange. If you buy $X$ flower pots of kind 1 then you must pay $A\times X^2$ and $B\times Y^2$ if you buy $Y$ flower pots of kind 2. Please help Creatnx buys exactly $N$ flower pots that minimizes money he pays.

Input Format

The first line contains a integer $T$ denoting the number of test cases.

Each of test case is described in a single line containing three space-separated integers $N,A,B$.

Output Format

For each test case, print a single line containing the answer.