A Simpler Goodstein Sequence

Given a positive integer $n$, let the following process:
1) We start with base 2
2) Express $n$ in the current base
3) Increment the base by 1
4) Take the number $n$ in this new base and decrement it by 1
5) Go to step 2 until $n=0$.

Here an example for $n=4$

Step	Number	Base	Digits	Comments
1	4	2	1,0,0
2	8	3	2,2	8 = 1.3^3 + 0.3^1 + 0 - 1
3	9	4	2,1	9 = 2.4^1 + 2 - 1
4	10	5	2,0
5	11	6	1,5
6	11	7	1,4
7	11	8	1,3
8	11	9	1,2
9	11	10	1,1
10	11	11	1,0
11	11	12	11
12	10	13	10
13	9	14	9
14	8	15	8
15	7	16	7
16	6	17	6
17	5	18	5
18	4	19	4
19	3	20	3
20	2	21	2
21	1	22	1
22	0	23	Done!

We reach the value $0$ in $22$ steps. Let write $G(4)=22$

What is $G(1024)$?
Give your answer modulo $1000000007$

PS:
This is a variant of Problem 396.