There is a ball at the top-left corner of an $n \times m$ grid. The rows of the grid are numbered $1,2,\dots,n$ , and the columns are numbered $1,2,\dots,m$ .
The ball is initially moving diagonally away from the top-left corner. At every step, it moves one cell. Whenever the ball hits the border of the grid, it changes its direction.
What is the __cpLocation of the ball after $k$ steps and how many times has it changed direction?
The first line has an integer $t$ : the number of tests.
After this, there are $t$ lines. Each line has three integers $n$ , $m$ and $k$ : the size of the grid and the number of steps.
For each test, print three integers: the __cpLocation of the ball and the number of direction changes.
6 3 4 0 3 4 1 3 4 2 3 4 3 3 4 4 42 1337 123456789\n · · \n · · \n · · \n · · \n · · \n · · \n
1 1 0 2 2 0 3 3 1 2 4 2 1 3 3 34 300 3101295· · \n · · \n · · \n · · \n · · \n · · \n