National Project

题意翻译

工程队修长度为$n$的路，每天可以修长度为$1$的路或者跳过。每$g$天好天气以后是$b$天坏天气，然后又是$g$天好天气，$b$天坏天气，以此类推。在好天气修路长度至少为总长度的一半，求修完路所需的最小天数（包括跳过的天数）。

题目描述

Your company was appointed to lay new asphalt on the highway of length $ n $ . You know that every day you can either repair one unit of the highway (lay new asphalt over one unit of the highway) or skip repairing. Skipping the repair is necessary because of the climate. The climate in your region is periodical: there are $ g $ days when the weather is good and if you lay new asphalt these days it becomes high-quality pavement; after that, the weather during the next $ b $ days is bad, and if you lay new asphalt these days it becomes low-quality pavement; again $ g $ good days, $ b $ bad days and so on. You can be sure that you start repairing at the start of a good season, in other words, days $ 1, 2, \dots, g $ are good. You don't really care about the quality of the highway, you just want to make sure that at least half of the highway will have high-quality pavement. For example, if the $ n = 5 $ then at least $ 3 $ units of the highway should have high quality; if $ n = 4 $ then at least $ 2 $ units should have high quality. What is the minimum number of days is needed to finish the repair of the whole highway?

输入输出格式

输入格式

The first line contains a single integer $ T $ ( $ 1 \le T \le 10^4 $ ) — the number of test cases. Next $ T $ lines contain test cases — one per line. Each line contains three integers $ n $ , $ g $ and $ b $ ( $ 1 \le n, g, b \le 10^9 $ ) — the length of the highway and the number of good and bad days respectively.

输出格式

Print $ T $ integers — one per test case. For each test case, print the minimum number of days required to repair the whole highway if at least half of it should have high quality.

输入输出样例

输入样例 #1

3
5 1 1
8 10 10
1000000 1 1000000

输出样例 #1

5
8
499999500000

说明

In the first test case, you can just lay new asphalt each day, since days $ 1, 3, 5 $ are good. In the second test case, you can also lay new asphalt each day, since days $ 1 $ - $ 8 $ are good.