Arithmetic and geometric Progressions are 2 of the well known progressions in maths. Arithmetic progression (AP) is a set in which the difference between 2 numbers in constant. for eg, 1,3,5,7,9....In this series the difference between 2 numbers is 2.The task here is very simple indeed. You will be given the 3rd term , 3rd last term and the sum of the series. You need to print the length of the series & the series itself.

Input

The first line of the input contains an integer T denoting the number of test cases.
Each of the following t lines will have 3 number '3rd term' ,'3rd Last term' and 'sum'.

3rd term - is the 3rd term in the series
3rd Last term - is the 3rd term from the end in the series
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.
2nd line of the output should print the series numbers separated by single spaces.

Constraints

1 ≤ T ≤ 100
All numbers will be less than 10^16.
The series will have at least 7 elements.
In all the test cases all the series elements are positive integers.

Example
Input:
1
3 8 55

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

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