AP2

Arithmatic and geometric Progressions are 2 of the well known progressions in maths.

Arithmatic 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 print length of the series & 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 and

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

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- number of terms in the series.

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

Example

Input:
1
3 8 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)

#include <iostream>

using namespace std;

int main() {  
    int T;
    cin >> T;

    for(;T--;) {
        long long a3, an_2, Sn;
        cin >> a3 >> an_2 >> Sn;

        long long n = (2 * Sn) / (a3 + an_2),
                  d = (an_2 - a3) / (n - 5),
                  a = an_2 + 3 * d - n * d;

        cout << n << "\n";
        for (int i = 0; i < n; ++i) {
            cout << a + i * d << " ";
        }
        cout << "\n";
    }
    return 0;
}