Sort a Stack Problem Statement

You are provided with a stack consisting of 'N' integers. The goal is to sort this stack in descending order by utilizing recursion.

Allowed Stack Operations:

is_empty(S) : Check if the stack is empty.
push(S) : Add a new element to the stack.
pop(S) : Remove the top element from the stack.
top(S) : Get the value of the top element without removing it.

Input:

The initial input line includes the integer 'T', which indicates the number of test cases.
Each individual test case is composed of:
- The first line: an integer 'N' indicating the number of elements within the stack.
- The following line: 'N' space-separated integers representing the stack's elements.

Output:

The output for each test case must consist of 'N' space-separated integers presenting the stack after it has been sorted in descending order.

Example:

Input:

2
3
3 2 1
5
4 5 3 2 1

Output:

3 2 1
5 4 3 2 1

Constraints:

• 1 <= 'T' <= 100
• 1 <= 'N' <= 100
• 1 <= |'V'| <= 10⁹ (where |V| signifies the absolute value of any stack element)
• Use of loop constructs such as while or for is prohibited.
• Duplicate integers may exist within the stack.
• Stack elements can be negative, positive, or zero.
• Time limit: 1 sec

Note:

You are not required to print anything; the output is handled by the system. Concentrate on implementing the function.