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: Time Limit Exceeded)

n,q = gets.split.map &:to_i
s = gets.split(//).map &:to_i

def solve_two_five(n,q,s)
  n.times.inject(0) do |ans,i|
    ans += s[i] % q == 0 ? i + 1 : 0
  end
end

def solve(n,q,s)
  cnt = Array.new(q,0)
  per = 1
  cur = 0
  (n-1).downto(0) do |d|
    cur += s[d] * per
    per *= 10
    cnt[cur % q] += 1
  end

  ans = 0
  q.times do |i|
    ans += cnt[i] * (cnt[i] - 1) / 2
  end
  ans += cnt[0]
end

if q == 2 || q == 5
  puts solve_two_five(n,q,s)
else
  puts solve(n,q,s)
end