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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

#!/usr/bin/env python3
import sys
from collections import defaultdict

def solve(N: int, P: int, S: str):
    if 10%P == 0:
        sum = 0
        for i in range(1,N+1):
            if int(S[-i]) % P == 0:
                sum += (N-i)+1
        print(sum)
        return
    else:
        sArr = [0] * N
        C = 1
        counts = defaultdict(int)
        for i in range(1,N+1):
            if i == 1:
                sArr[i - 1] = int(S[-1])%P
            else:
                sArr[i-1]  = (int(S[-i])*C + sArr[i-2])%P
            counts[sArr[i-1]]+=1
            C*=10
        sum = 0
        for k in counts:
            c = counts[k]
            sum += int((c*(c-1)/2))
        sum += counts[0]
        print(sum)

    # sum = 0
    # for i in range(N):
    #     sDiv = 0
    #     coeff = 1
    #     for j in range(i,N):
    #         sDiv= (sDiv*coeff + arr[j])%P
    #         coeff*=10
    #         if sDiv == 0:
    #             sum+=1
    # print(sum)
    return


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    P = int(next(tokens))  # type: int
    S = next(tokens)  # type: int
    solve(N, P, S)

if __name__ == '__main__':
    main()