Special Shop

3.8

135 votes
Algorithms, Easy, Searching, differentiation
Problem

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×X2 and B×Y2 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.

Constraints

  • 1T105
  • 1N,A,B105

 

Time Limit: 1
Memory Limit: 256
Source Limit:
Explanation

Query 1: we have to buy exactly 5 pots. There are six possible options:

  • Buy 0 pot of first kind, 5 pots of second kind. The cost is: 1×02+2×52=50.
  • Buy 1 pot of first kind, 4 pots of second kind. The cost is: 1×12+2×42=33.
  • Buy 2 pots of first kind, 3 pots of second kind. The cost is: 1×22+2×32=22.
  • Buy 3 pots of first kind, 2 pots of second kind. The cost is: 1×32+2×22=17.
  • Buy 4 pots of first kind, 1 pot of second kind. The cost is: 1×42+2×12=18.
  • Buy 5 pots of first kind, 0 pot of second kind. The cost is: 1×52+2×02=25.

So, the optimal cost is 17.

Editor Image

?