Algorithm for counting substrings in a numerical range

Algorithm for counting substrings in a numerical range

I'm looking for a fast algorithm that can be used to solve this problem:
Giving A and B integers (in the range [0,10^18]), and giving a list of N
(N<=1000) numerical substrings; the goal is to count all the numbers in
the range [A,B] containing any of the N substrings. We've always A<=B and
the numerical substrings are also integers in the range [0,10^18].
Example1: if A=10, B=22, and giving N=2 substrings={1,10} ; the count
would be = 11; counting the numbers: 10->19 and 21.
Example2: If A=175, B=201, and giving N=3 substrings={55,0,200} ; the
count would be = 4; counting the numbers: 180, 190, 200 and 201.
The straight-forward way is to analyse each integer in the range [A,B],
one after another, but it's not a solution since the range can be so big
(until 10^18 integers).
One first thing I did to reduce the problem complexity is to delete some
useless substrings from the original list of N substrings, such that "no
substring is contained in another". For example: {1,10} becomes {1} and
{55,0,200} becomes {55,0}. This won't change the final count.
Next, even assuming we can get the count for one substring in the range
[A,B], we still cannot sum this count with those of other substrings from
the list, as one number can contain many substrings and should not be
counted more than once.
Any ideas to solve the problem et get the wanted count?
Thanks