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
# -*- coding: utf-8 -*-

from functools import lru_cache


def main():
    n, p = map(int, input().split())
    s = input().strip()
    mod_dict.clear()

    ans = 0
    for i in range(n):
        for j in range(i, n):
            if is_mod_zero(s, i, j, p):
                ans += 1
    print(ans)


mod_dict = {}


def is_mod_zero(s, i, j, p):
    c = int(s[i:j + 1])
    if c in mod_dict:
        return mod_mem(c, p) == 0
    if c == 0:
        return True
    if c < p:
        return False
    if i == j:
        return mod_mem(int(s[i]), p) == 0
    if c < 100:
        return mod_mem(c, p) == 0

    prev_c = int(s[i:j])
    new_c = int(s[j])
    tp = mod_mem(10, p)

    prev_c_mod = mod_mem(prev_c, p)
    new_c_mod = mod_mem(new_c, p)

    c_mod = ((tp * prev_c_mod) % p + new_c_mod) % p
    mod_dict[c] = c_mod
    return c_mod == 0


def mod_mem(a, p):
    if a in mod_dict:
        return mod_dict[a]

    a_mod = a % p
    mod_dict[a] = a_mod
    return a_mod


if __name__ == '__main__':
    main()