Codeforces Round 834 (Div. 3) |
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Finished |
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.
103 5 63 30 15 54 50 10 53 73 5 63 4-10 10 11-5 6-3 3 41 0-5 10 89 21 5 12 5-1 4 30 2-6 3 6-1 -4
0 2 3 -1 1 -1 3 1 3 -1
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.
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