CF773A.Success Rate

You are an experienced Codeforces user. Today you found out that during your activity on Codeforces you have made y submissions, out of which x have been successful. Thus, your current success rate on Codeforces is equal to x / y.

Your favorite rational number in the [0;1] range is p / q. Now you wonder: what is the smallest number of submissions you have to make if you want your success rate to be p / q?

你是一名经验丰富的 Codeforces 用户。今天你发现，在 Codeforces 上的活动期间，你总共提交了 $y$ 次，其中成功的提交有 $x$ 次。因此，你当前在 Codeforces 上的成功率为 $x\,/\,y$。

你在 $[0;1]$ 范围内最喜爱的有理数是 $p\,/\,q$。现在你想知道：若希望你的成功率达到 $p\,/\,q$，你至少还需要进行多少次提交？

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

Each of the next t lines contains four integers x, y, p and q (0 ≤ x ≤ y ≤ 109; 0 ≤ p ≤ q ≤ 109; y > 0; q > 0).

It is guaranteed that p / q is an irreducible fraction.

Hacks. For hacks, an additional constraint of t ≤ 5 must be met.

第一行包含一个整数 $t$（$1 \leq t \leq 1000$）—— 表示测试用例的数量。

接下来的 $t$ 行，每行包含四个整数 $x$、$y$、$p$ 和 $q$（$0 \leq x \leq y \leq 10^9$；$0 \leq p \leq q \leq 10^9$；$y > 0$；$q > 0$）。

保证 $\frac{p}{q}$ 是一个最简分数。

Hack 数据要求：对于 Hack 数据，需额外满足约束 $t \leq 5$。

For each test case, output a single integer equal to the smallest number of submissions you have to make if you want your success rate to be equal to your favorite rational number, or -1 if this is impossible to achieve.

对于每个测试用例，输出一个整数，表示为使你的成功率等于你最喜欢的有理数所需提交的最少次数；若无法实现，则输出 $-1$。

In the first example, you have to make 4 successful submissions. Your success rate will be equal to 7 / 14, or 1 / 2.

In the second example, you have to make 2 successful and 8 unsuccessful submissions. Your success rate will be equal to 9 / 24, or 3 / 8.

In the third example, there is no need to make any new submissions. Your success rate is already equal to 20 / 70, or 2 / 7.

In the fourth example, the only unsuccessful submission breaks your hopes of having the success rate equal to 1.

在第一个例子中，你需要进行 4 次成功的提交。你的成功率将等于 $7/14$，即 $1/2$。

在第二个例子中，你需要进行 2 次成功的提交和 8 次失败的提交。你的成功率将等于 $9/24$，即 $3/8$。

在第三个例子中，无需进行任何新的提交。你的成功率已经等于 $20/70$，即 $2/7$。

在第四个例子中，唯一一次失败的提交使你无法达成成功率等于 $1$ 的目标。