This is the eightieth second part of the ILP series. For your convenience you can find other parts in the table of contents in Part 1 – Boolean algebra
Today we’re going to solve S and P. The idea is: we start with two non-negative integers 
and 
. We calculate 
and 
. Now we take digits of 
and 
and want all of them to be distinct and form a continuous sequence after sorting. For instance, for 
and 
we get 
and 
so digits are 
which are distinct and form a proper sequence.
We want to find a solution for some 
indicating how long the sequence should be.
Solution:
We start with definition of in line 1.
Next, we calculate how many digits there are in the sum and in result of multiplication. We assume the latter is bigger than the former.
Next, we define initial variables (lines 6-7) and calculations (9-10).
Next, we extract digits in base 10. We make sure that the result of decomposition is not too big (lines 17-20 and 29-32). We basically zero-out too big digits.
Next, we make sure that the decomposition is not too low. So the most significant digit must be non-zero (lines 21 and 33).
Finally, we take all digits and make sure they are distinct (line 39). Next, we calculate min and max (41-42) and then make sure that they differ by 
. Since all digits are distinct, we get the required effect.
Output: