After solving "AP - Complete The Series (easy)" very fast, Lucifer decided to make it little more interesting.

He said

He will be give you the 3rd term, 4th last term and the sum of the AP series. You need print length of the series and the series.

Input

First line will contain a number indicating the number of test cases.

Each of the following t lines will have 3 number '3term' ,'4Lastterm' and 'sum'

3term  - is the 3rd term in the series and

4Lastterm  - is the 4th last term in the series and

sum - is the sum of the series.

Output

For each input of the test case, you need to print 2 lines.

first line should have 1 value - number of terms in the series.

second line of the output should print the series numbers separated by single space.

Example

Input:
1
3 7 55

Output:
10
1 2 3 4 5 6 7 8 9 10

NOTE

In all the test cases all the series elements are positive integers.

The series will have at least 7 elements.

Number of test cases <=100.

All the numbers will fit in 64 bits (long long in C)