CF1759C.Thermostat

Vlad came home and found out that someone had reconfigured the old thermostat to the temperature of $a$ .

The thermostat can only be set to a temperature from $l$ to $r$ inclusive, the temperature cannot change by less than $x$ . Formally, in one operation you can reconfigure the thermostat from temperature $a$ to temperature $b$ if $|a - b| \ge x$ and $l \le b \le r$ .

You are given $l$ , $r$ , $x$ , $a$ and $b$ . Find the minimum number of operations required to get temperature $b$ from temperature $a$ , or say that it is impossible.

The first line of input data contains the single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases in the test.

The descriptions of the test cases follow.

The first line of each case contains three integers $l$ , $r$ and $x$ ( $-10^9 \le l \le r \le 10^9$ , $1 \le x \le 10^9$ ) — range of temperature and minimum temperature change.

The second line of each case contains two integers $a$ and $b$ ( $l \le a, b \le r$ ) — the initial and final temperatures.

Output $t$ numbers, each of which is the answer to the corresponding test case. If it is impossible to achieve the temperature $b$ , output -1, otherwise output the minimum number of operations.

In the first example, the thermostat is already set up correctly.

In the second example, you can achieve the desired temperature as follows: $4 \rightarrow 10 \rightarrow 5$ .

In the third example, you can achieve the desired temperature as follows: $3 \rightarrow 8 \rightarrow 2 \rightarrow 7$ .

In the fourth test, it is impossible to make any operation.