A12748. Maximum Sine
编程题
普及/提高-
知识点
题目描述
You have given integers $a$ , $b$ , $p$ , and $q$ . Let $f(x) = \text{abs}(\text{sin}(\frac{p}{q} \pi x))$ .
Find minimum possible integer $x$ that maximizes $f(x)$ where $a \le x \le b$ .
Find minimum possible integer $x$ that maximizes $f(x)$ where $a \le x \le b$ .
输入格式
Each test contains multiple test cases.
The first line contains the number of test cases $t$ ( $1 \le t \le 100$ ) — the number of test cases.
The first line of each test case contains four integers $a$ , $b$ , $p$ , and $q$ ( $0 \le a \le b \le 10^{9}$ , $1 \le p$ , $q \le 10^{9}$ ).
The first line contains the number of test cases $t$ ( $1 \le t \le 100$ ) — the number of test cases.
The first line of each test case contains four integers $a$ , $b$ , $p$ , and $q$ ( $0 \le a \le b \le 10^{9}$ , $1 \le p$ , $q \le 10^{9}$ ).
输出格式
Print the minimum possible integer $x$ for each test cases, separated by newline.
输入输出样例
输入 #1
2 0 3 1 3 17 86 389 995
输出 #1
1 55
说明/提示
In the first test case, $f(0) = 0$ , $f(1) = f(2) \approx 0.866$ , $f(3) = 0$ .
In the second test case, $f(55) \approx 0.999969$ , which is the largest among all possible values.
In the second test case, $f(55) \approx 0.999969$ , which is the largest among all possible values.