CF1765E.Exchange

Monocarp is playing a MMORPG. There are two commonly used types of currency in this MMORPG — gold coins and silver coins. Monocarp wants to buy a new weapon for his character, and that weapon costs $n$ silver coins. Unfortunately, right now, Monocarp has no coins at all.

Monocarp can earn gold coins by completing quests in the game. Each quest yields exactly one gold coin. Monocarp can also exchange coins via the in-game trading system. Monocarp has spent days analyzing the in-game economy; he came to the following conclusion: it is possible to sell one gold coin for $a$ silver coins (i. e. Monocarp can lose one gold coin to gain $a$ silver coins), or buy one gold coin for $b$ silver coins (i. e. Monocarp can lose $b$ silver coins to gain one gold coin).

Now Monocarp wants to calculate the minimum number of quests that he has to complete in order to have at least $n$ silver coins after some abuse of the in-game economy. Note that Monocarp can perform exchanges of both types (selling and buying gold coins for silver coins) any number of times.

Monocarp 正在玩一款大型多人在线角色扮演游戏（MMORPG）。该游戏中有两种常用货币——金币和银币。Monocarp 想为自己的角色购买一件新武器，该武器售价为 $n$ 枚银币。不幸的是，此时 Monocarp 手中一枚硬币也没有。

Monocarp 可以通过完成游戏中的任务来获取金币，每项任务恰好奖励一枚金币。Monocarp 还可以通过游戏内的交易系统进行货币兑换。Monocarp 已花费数日分析游戏内经济系统，并得出如下结论：他可以将一枚金币卖出，换取 $a$ 枚银币（即 Monocarp 放弃一枚金币，获得 $a$ 枚银币），也可以用 $b$ 枚银币购买一枚金币（即 Monocarp 放弃 $b$ 枚银币，获得一枚金币）。

现在，Monocarp 想计算：为了在充分利用游戏内经济系统后，最终至少拥有 $n$ 枚银币，他最少需要完成多少项任务？注意，Monocarp 可以任意多次执行两种类型的兑换操作（即出售金币换银币、或用银币购买金币）。

The first line contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

Each test case consists of one line containing three integers $n$, $a$ and $b$ ($1 \le n \le 10^7$; $1 \le a, b \le 50$).

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。

每个测试用例由一行组成，包含三个整数 $n$、$a$ 和 $b$（$1 \le n \le 10^7$；$1 \le a, b \le 50$）。

For each test case, print one integer — the minimum possible number of quests Monocarp has to complete.

对于每个测试用例，输出一个整数——Monocarp 需要完成的最少任务数量。

In the first test case of the example, Monocarp should complete $4$ quests, and then sell $4$ gold coins for $100$ silver coins.

In the second test case, Monocarp should complete $400000$ quests, and then sell $400000$ gold coins for $10$ million silver coins.

In the third test case, Monocarp should complete $1$ quest, sell the gold coin for $50$ silver coins, buy a gold coin for $48$ silver coins, and then sell it again for $50$ coins. So, he will have $52$ silver coins.

In the fourth test case, Monocarp should complete $1$ quest and then sell the gold coin he has obtained for $50$ silver coins.

在示例的第一个测试用例中，Monocarp 应完成 $4$ 个任务，然后将 $4$ 枚金币出售，换取 $100$ 枚银币。

在第二个测试用例中，Monocarp 应完成 $400000$ 个任务，然后将 $400000$ 枚金币出售，换取 $1000$ 万枚银币。

在第三个测试用例中，Monocarp 应完成 $1$ 个任务，将获得的金币以 $50$ 枚银币的价格售出，再以 $48$ 枚银币的价格购回一枚金币，最后再次以 $50$ 枚银币的价格售出。因此，他最终将拥有 $52$ 枚银币。

在第四个测试用例中，Monocarp 应完成 $1$ 个任务，然后将获得的金币以 $50$ 枚银币的价格售出。