Geometric progression (GP) is a set in which the ratio of 2 consecutive numbers is same. for example: 1, 2, 4, 8, 16 - in this case, the ratio of the 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 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', '3Lastterm' and 'sum'

3term - is the 3rd term in of the series,

3Lastterm - is the 3rd to last term of the series,

sum - is the sum of the series.

Output

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

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

2nd line of the output should print the series numbers separated by single space.

Example

Input:
1
4 64 511

Output:
9
1 2 4 8 16 32 64 128 256

NOTE

• All the values will be in the range [0, 2⁶⁴] inclusive.
• The series will have at least 6 elements.
• Number of test cases ≤ 100.
• The ratio in all cases will be an integer. (Thanks Mitch for pointing this out.)
• All the numbers will fit in 64 bits (long long in C.)