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 PyPy3 (2.4.0) (judge verdict: Accepted)

def main():
  N,P = map(int,input().split())
  S = input()

  ans = 0
  if P == 2 or P == 5:
    for i in range(N):
      if int(S[i])%P == 0:
        ans += i+1
  else:
    # r = [0] * (N+1)
    # for i in range(N):
    #   r[N-1-i] = int(S[N-1-i:])%P
    # for i in range(N):
    #   for j in range(i,N):
    #     if (r[i]-r[j+1])%P == 0:
    #       ans += 1
    d = {}
    r = 0
    for i in range(N):
      # r = int(S[N-1-i:])%P
      # とするとTLEになってしまう。
      r = (r + int(S[N-1-i])*pow(10,i,P))%P
      if r in d:
        d[r] += 1
      else:
        d[r] = 1
    if 0 in d:
      d[0] += 1
    for k,v in d.items():
      ans += v*(v-1)//2
  
  print(ans)

if __name__ == '__main__':
  main()