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 (3.8.2) (judge verdict: Accepted)

from math import gcd
from collections import defaultdict

N, P = map(int, input().split())
S = list(map(int, input()))

answer = 0
if P == 2 or P == 5:
    for j in range(N - 1, -1, -1): # enumerate right endpoint
        if S[j] % P == 0:
            answer += j + 1
else:
    cnts = defaultdict(int)
    suffix = 0
    base = 1
    for i in range(N - 1, -1, -1):
        suffix = (suffix + S[i] * base) % P
        answer += cnts[suffix]  # Substr with length >= 2
        answer += 1 if suffix == 0 else 0 # Substr with length = 1
        cnts[suffix] += 1
        base = base * 10 % P

print(answer)