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.