brainfuck, 26 bytes

+[[>>++<,.<-]+++++++++.>>]

Attempt This Online!

Output separated by tabs (ASCII 9) with some extra tabs at the end.

brainfuck, 26 bytes

+[[->,.>++<<]+++++++++.>>]

Attempt This Online!

Output separated by tabs with some extra tabs at the end.

This is pretty short so I may as well add an explanation:

+        1 is the first segment length
[  
  [-     Repeat that many times:
    >,.    Go right: read and output one character
    >++    Go right: Add two to this cell
             (This is what doubles the length)
    <<]    Go back to the loop counter cell
  +++++  The cell is now zero so we can freely
  ++++.    change it; output a tab (ASCII 9)
  >>]    Go to our new loop counter cell and start
           again