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: Time Limit Exceeded)

def main():
    import collections
    N, P = map(int, input().split())
    S = input()[::-1]
    ans = 0
    if P == 2 or P == 5:
        for i, s in enumerate(S):
            if int(s) % P == 0:
                ans += N - i
    else:
        D = [0] * N
        A = [0] * (N + 1)
        for i, s in enumerate(S):
            D[i] = int(s) * 10 ** i % P
            if i == 0:
                A[i] = D[i]
            else:
                A[i] = (D[i] + A[i - 1]) % P
        c = collections.Counter(A)
        ans = sum([i * (i - 1) // 2 for i in c.values()])
    
    print(ans)

if __name__ == '__main__':
    main()