Thermostat

Description:

Input:

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:

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.

Sample Input:

10
3 5 6
3 3
0 15 5
4 5
0 10 5
3 7
3 5 6
3 4
-10 10 11
-5 6
-3 3 4
1 0
-5 10 8
9 2
1 5 1
2 5
-1 4 3
0 2
-6 3 6
-1 -4

Sample Output:

0
2
3
-1
1
-1
3
1
3
-1

Note:

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.