Buying Torches

题意翻译

## 题目描述： 你要获得 $k$ 个火把，最开始你有 $1$ 根木棒。一个木棒和一个煤炭可以合成一个火把，你也可以通过两种交易方式得到木棒或煤炭： 1. 通过**给**商人 $1$ 根木棒，获得 $x$ 根木棒。 1. 通过**给**商人 $y$ 根木棒，获得 $1$ 个煤炭。 其中 $2\leq x\leq 10^{9};1\leq y,k\leq 10^{9}$。 求得到 $k$ 个火把的最少交易次数。

题目描述

You are playing a very popular game called Cubecraft. Initially, you have one stick and want to craft $ k $ torches. One torch can be crafted using one stick and one coal. Hopefully, you've met a very handsome wandering trader who has two trade offers: - exchange $ 1 $ stick for $ x $ sticks (you lose $ 1 $ stick and gain $ x $ sticks). - exchange $ y $ sticks for $ 1 $ coal (you lose $ y $ sticks and gain $ 1 $ coal). During one trade, you can use only one of these two trade offers. You can use each trade offer any number of times you want to, in any order. Your task is to find the minimum number of trades you need to craft at least $ k $ torches. The answer always exists under the given constraints. You have to answer $ t $ independent test cases.

输入输出格式

输入格式

The first line of the input contains one integer $ t $ ( $ 1 \le t \le 2 \cdot 10^4 $ ) — the number of test cases. Then $ t $ test cases follow. The only line of the test case contains three integers $ x $ , $ y $ and $ k $ ( $ 2 \le x \le 10^9 $ ; $ 1 \le y, k \le 10^9 $ ) — the number of sticks you can buy with one stick, the number of sticks required to buy one coal and the number of torches you need, respectively.

输出格式

For each test case, print the answer: the minimum number of trades you need to craft at least $ k $ torches. The answer always exists under the given constraints.

输入输出样例

输入样例 #1

5
2 1 5
42 13 24
12 11 12
1000000000 1000000000 1000000000
2 1000000000 1000000000

输出样例 #1

14
33
25
2000000003
1000000001999999999