CF2180A.Carnival Wheel

You have a prize wheel divided into $l$ sections, numbered from $0$ to $l-1$. The sections are arranged in a circle, so after section $l-1$, the numbering continues again from section $0$.

Initially, the prize pointer is at section $a$. Each time you spin the wheel, the pointer moves exactly $b$ sections forward. That is, after one spin, the pointer moves from section $a$ to section $(a+b)\bmod l$, after two spins to $(a+2b)\bmod l$, and so on$^{\text{∗}}$.

You may spin the wheel any number of times (including zero). After you stop, the section where the pointer finally lands determines your prize: you receive an amount equal to the number of that section.

What is the maximum prize you can obtain?

$^{\text{∗}}$Here, $x \bmod y$ denotes the remainder from dividing $x$ by $y$.

你有一个被分为 $l$ 个扇形区域的奖品转盘，区域编号从 $0$ 到 $l-1$。这些区域呈环形排列，因此在区域 $l-1$ 之后，编号再次从区域 $0$ 开始。

初始时，指针位于区域 $a$。每次旋转转盘，指针恰好向前移动 $b$ 个区域。即：旋转一次后，指针从区域 $a$ 移动到区域 $(a+b)\bmod l$；旋转两次后移动到 $(a+2b)\bmod l$，依此类推$^{\text{∗}}$。

你可以任意次数地旋转转盘（包括零次）。当你停止旋转后，指针最终停留的区域编号即为你获得的奖品金额。

你能获得的最大奖品金额是多少？

$^{\text{∗}}$此处，$x \bmod y$ 表示 $x$ 除以 $y$ 所得的余数。

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 500$). The description of the test cases follows.

The first line of each test case contains three integers $l, a$, and $b$ ($1 \le l, b \le 5000$, $0 \le a \le l-1$).

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 500$）。随后是各测试用例的描述。

每个测试用例的第一行包含三个整数 $l$、$a$ 和 $b$（$1 \le l, b \le 5000$，$0 \le a \le l-1$）。

For each test case, output the maximum prize that can be obtained.

对于每个测试用例，输出能够获得的最大奖品价值。

In the first test case, by spinning the wheel three times and then claiming the reward, you can obtain a maximum value of $4$. The sequence of pointer positions is: $3, 0, 2, 4, 1, 3, 0, \ldots$

In the second test case, the pointer will remain on section $0$ indefinitely.

In the fourth test case, with $b = 1$ and starting from section $0$, the pointer will iterate over all sections, including the last one.

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在第一个测试用例中，通过旋转转盘三次后领取奖励，可以获得最大值 $4$。指针位置序列为：$3, 0, 2, 4, 1, 3, 0, \ldots$

在第二个测试用例中，指针将无限停留在第 $0$ 区域。

在第四个测试用例中，当 $b = 1$ 且从第 $0$ 区域开始时，指针将遍历所有区域（包括最后一个区域）。

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