30166번 - Maximum Sine 다국어

문제

You have given integers $a,ドル $b,ドル $p,ドル and $q$. Let $f(x) = \text{abs}(\text{sin}(\frac{p}{q} \pi x))$.

Find minimum possible integer $x$ that maximizes $f(x)$ where $a \le x \le b$.

입력

Each test contains multiple test cases.

The first line contains the number of test cases $t$ (1ドル \le t \le 100$) --- the number of test cases.

The first line of each test case contains four integers $a,ドル $b,ドル $p,ドル and $q$ (0ドル \le a \le b \le 10^{9},ドル 1ドル \le p,ドル $q \le 10^{9}$).

출력

Print the minimum possible integer $x$ for each test cases, separated by newline.

제한

노트

In the first test case, $f(0) = 0,ドル $f(1) = f(2) \approx 0.866,ドル $f(3) = 0$.

In the second test case, $f(55) \approx 0.999969,ドル which is the largest among all possible values.