Let's learn about list comprehensions! You are given three integers $x,y$ and $z$ representing the dimensions of a cuboid along with an integer $n.$ Print a list of all possible coordinates given by $(i,j,k)$ on a $3$D grid where the sum of $i+j+k$ is not equal to $n.$ Here, $0ix$;$0jy$;$0kz.$ Please use list comprehensions rather than multiple loops, as a learning exercise.

Example

$x=1$

$y=1$

$z=2$

$n=3$

All permutations of $i,j,k$ are:

Print an array of the elements that do not sumiton $3.{?}_3$

Input Format

Four integers $x,y,z$ and $n,$ each on a separate line.

Constraints

Print the list in lexicographic increasing order.

Sample Input $0$