CF1418A.Buying Torches

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.

你正在玩一款非常流行的游戏，名为“方块工艺”（Cubecraft）。初始时，你拥有 1 根木棍，目标是制作 $k$ 把火把。每把火把需要消耗 1 根木棍和 1 块煤炭。

幸运的是，你遇到了一位英俊的流浪商人，他提供了两种交易选项：

• 用 $1$ 根木棍换取 $x$ 根木棍（你失去 $1$ 根木棍，获得 $x$ 根木棍）；
• 用 $y$ 根木棍换取 $1$ 块煤炭（你失去 $y$ 根木棍，获得 $1$ 块煤炭）。

每次交易中，你只能选择上述两种交易选项之一。你可以以任意顺序、任意次数使用任一交易选项。

你的任务是求出制作至少 $k$ 把火把所需的最少交易次数。在给定约束下，答案一定存在。

你需要回答 $t$ 个相互独立的测试用例。

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.

输入的第一行包含一个整数 $t$（$1 \le t \le 2 \cdot 10^4$），表示测试用例的数量。接下来是 $t$ 个测试用例。

每个测试用例仅有一行，包含三个整数 $x$、$y$ 和 $k$（$2 \le x \le 10^9$；$1 \le y, k \le 10^9$），分别表示用一根木棍可购买的木棍数量、购买一块煤炭所需的木棍数量，以及你需要的火把数量。

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.

对于每个测试用例，输出答案：至少制作 $k$ 把火把所需的最少交易次数。在给定约束条件下，答案一定存在。