CF1082A.Vasya and Book

Vasya is reading a e-book. The file of the book consists of $n$ pages, numbered from $1$ to $n$. The screen is currently displaying the contents of page $x$, and Vasya wants to read the page $y$. There are two buttons on the book which allow Vasya to scroll $d$ pages forwards or backwards (but he cannot scroll outside the book). For example, if the book consists of $10$ pages, and $d = 3$, then from the first page Vasya can scroll to the first or to the fourth page by pressing one of the buttons; from the second page — to the first or to the fifth; from the sixth page — to the third or to the ninth; from the eighth — to the fifth or to the tenth.

Help Vasya to calculate the minimum number of times he needs to press a button to move to page $y$.

瓦西娅正在阅读一本电子书。该书的文件包含 $n$ 页，页码从 $1$ 到 $n$。当前屏幕显示的是第 $x$ 页的内容，而瓦西娅希望阅读第 $y$ 页。电子书上有两个按钮，分别允许瓦西娅向前或向后翻阅 $d$ 页（但他不能翻出书的范围）。例如，若该书共有 $10$ 页，且 $d = 3$，则：从第 $1$ 页出发，按一次按钮可到达第 $1$ 页（无法向前翻）或第 $4$ 页；从第 $2$ 页出发，可到达第 $1$ 页或第 $5$ 页；从第 $6$ 页出发，可到达第 $3$ 页或第 $9$ 页；从第 $8$ 页出发，可到达第 $5$ 页或第 $10$ 页。

请帮助瓦西娅计算他最少需要按多少次按钮才能到达第 $y$ 页。

The first line contains one integer $t$ ($1 \le t \le 10^3$) — the number of testcases.

Each testcase is denoted by a line containing four integers $n$, $x$, $y$, $d$ ($1\le n, d \le 10^9$, $1 \le x, y \le n$) — the number of pages, the starting page, the desired page, and the number of pages scrolled by pressing one button, respectively.

第一行包含一个整数 $t$（$1 \le t \le 10^3$）—— 测试用例的数量。

每个测试用例由一行表示，该行包含四个整数 $n$、$x$、$y$、$d$（$1\le n, d \le 10^9$，$1 \le x, y \le n$）—— 分别表示总页数、起始页、目标页以及按一次按钮所滚动的页数。

Print one line for each test.

If Vasya can move from page $x$ to page $y$, print the minimum number of times he needs to press a button to do it. Otherwise print $-1$.

每个测试用例输出一行。

如果瓦西娅可以从第 $x$ 页移动到第 $y$ 页，则输出他需要按按钮的最少次数；否则输出 $-1$。

In the first test case the optimal sequence is: $4 \rightarrow 2 \rightarrow 1 \rightarrow 3 \rightarrow 5$.

In the second test case it is possible to get to pages $1$ and $5$.

In the third test case the optimal sequence is: $4 \rightarrow 7 \rightarrow 10 \rightarrow 13 \rightarrow 16 \rightarrow 19$.

在第一个测试用例中，最优序列为：$4 \rightarrow 2 \rightarrow 1 \rightarrow 3 \rightarrow 5$。

在第二个测试用例中，可以到达页面 $1$ 和 $5$。

在第三个测试用例中，最优序列为：$4 \rightarrow 7 \rightarrow 10 \rightarrow 13 \rightarrow 16 \rightarrow 19$。