Greater Integer, Better LCM

题号：NC222405
时间限制：C/C++/Rust/Pascal 2秒，其他语言4秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

Given three positive integers $a,b,c~(a,b \le c)$ , you should find two non-negative integers $x,y_{}$ that $\mathrm{lcm}(a+x, b+y) = c_{}$ and minimize $x+y_{}$ . Print the minimum $x+y_{}$ . Here $c_{}$ will be given in format $\prod_{i=1}^{n}{p_i}^{q_i}$ where $p_i, q_i$ denotes the primary factor and its power respectively.

Hint: you can use "__int128_t" in C++ to handle 128-bit integers.

输入描述:

The first line contains one integer .

Following  lines each contains two integers .

Following one line contains two integers , where .

It's guaranteed that s are all primes and .

输出描述:

Output one line only containing one integer, denoting the answer.

示例1

输入

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输出

复制

说明

, and one possible scheme is : .