Problem:
Score : 500 points

Problem Statement

Takahashi has a string S of length N consisting of digits from 0 through 9.

He loves the prime number P. He wants to know how many non-empty (contiguous) substrings of S - there are N \times (N + 1) / 2 of them - are divisible by P when regarded as integers written in base ten.

Here substrings starting with a 0 also count, and substrings originated from different positions in S are distinguished, even if they are equal as strings or integers.

Compute this count to help Takahashi.

Constraints

1 \leq N \leq 2 \times 10^5

S consists of digits.

|S| = N

2 \leq P \leq 10000

P is a prime number.

Input

Input is given from Standard Input in the following format:

N P
S

Output

Print the number of non-empty (contiguous) substrings of S that are divisible by P when regarded as an integer written in base ten.

Sample Input 1

4 3
3543

Sample Output 1

6

Here S = 3543. There are ten non-empty (contiguous) substrings of S:

3: divisible by 3.

35: not divisible by 3.

354: divisible by 3.

3543: divisible by 3.

5: not divisible by 3.

54: divisible by 3.

543: divisible by 3.

4: not divisible by 3.

43: not divisible by 3.

3: divisible by 3.

Six of these are divisible by 3, so print 6.

Sample Input 2

4 2
2020

Sample Output 2

10

Here S = 2020. There are ten non-empty (contiguous) substrings of S, all of which are divisible by 2, so print 10.

Note that substrings beginning with a 0 also count.

Sample Input 3

20 11
33883322005544116655

Sample Output 3

68

Solution in Ruby (2.3.3) (judge verdict: Accepted)

N, P = gets.split.map(&:to_i)
S = gets.chomp.split('')
result = 0
if P == 2
  S.length.times do |i|
    if S[i].to_i.even?
      result += i + 1
    end
  end
  puts result
  exit
end

if P == 5
  S.length.times do |i|
    if [5,0].include?(S[i].to_i)
      result += i + 1
    end
  end
  puts result
  exit
end

mod_counts = {}
mods = []
s_length = S.length
mod_counts[0] = 1
mod = 0

@fact10 = {}
def fact10 x
  return 1 if x == 0
  unless @fact10[x]
    @fact10[x] = (fact10(x-1) * 10) % P
  end
  @fact10[x]
end
s_length.times do |i|
  target = S[(s_length - 1 -i)].to_i
  mod = (mod + target * fact10(i)) % P
  if mod_counts[mod]
    result += mod_counts[mod]
    mod_counts[mod] += 1
  else
    mod_counts[mod] = 1
  end
end

puts result