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)

def main():
    from collections import Counter
    N, P = (int(i) for i in input().split())
    S = input()

    ans = 0
    if P == 5 or P == 2:
        for j in range(1, N+1):
            # j文字取る
            num = int(S[:j])
            if num % P == 0:
                ans += j
    else:
        acc = [0]*(N+1)
        d = 1
        for i, s in enumerate(S[::-1], start=1):
            # print(i, s)
            acc[i] = (int(s) * d + acc[i-1]) % P
            d *= 10
            d %= P
        c = Counter(acc)
        # print(acc, c)
        ans = sum(v*(v-1)//2 for v in c.values())
    print(ans)


if __name__ == '__main__':
    main()