ZOJ - 3593 One Person Game （扩展欧几里得 技巧）@

There is an interesting and simple one person game. Suppose there is a number axis under your feet. You are at point A at first and your aim is point B. There are 6 kinds of operations you can perform in one step. That is to go left or right by a,band c, here c always equals to a+b.

You must arrive B as soon as possible. Please calculate the minimum number of steps.

Input

There are multiple test cases. The first line of input is an integer T(0 < T ≤ 1000) indicates the number of test cases. Then T test cases follow. Each test case is represented by a line containing four integers 4 integers A, B, a and b, separated by spaces. (-2³¹ ≤ A, B < 2³¹, 0 < a, b < 2³¹)

Output

For each test case, output the minimum number of steps. If it's impossible to reach point B, output "-1" instead.

Sample Input

2
0 1 1 2
0 1 2 4

Sample Output

1
-1

题意：给你一个起点和终点，每次可以向左或向右走a步或b或c步，c=a+b;问最小步数；

根据公式ax+by=c;，当x,y同号时等于max（x,y）,当a,b异号时等于（abs(x)+abs(y)）,因为a,b大于0，所以不管x,y同号还是异号都是当x,y,最接近时，答案最小，写出通式

x=x1+b/(gcd)*k,y=y1-a/gcd*k; 假设x,y相等,k=(y-x)/(a+b),因为x,y不一定相等,所以枚举k附近的点

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