My solution is not very elegant. It may not even be right. But here goes.
First I seek an upper bound to the solution.
Now we conclude that has 17 digits where the most significant digit is 1 and the other digits are unknown (but not more than 9).
Now for all numbers up to 145 the one with the largest digit sum is 139 which sums to 13. Hence B<13.
Now summing the digits of any number gives a result that is equal to the starting number (modulo 9).
Hence (mod 9)
This is greater than 13 so I sum the digits repeatidly until I get an acceptable answer. The result is 823543, 25, 7. OK so I think the answer is 7.
When you receive the model answer can you please post it?