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 Rust (1.15.1) (judge verdict: Time Limit Exceeded)

use std::io::Read;
use std::collections::HashMap;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let p: usize = iterator.next().unwrap().parse().unwrap();

    let s = iterator.next().unwrap();

    let mut memo: HashMap<String, usize> = HashMap::new();

    let mut ans: usize = 0;
    for i in 1..(n + 1) {
        for j in 0..(n - i + 1) {
            if is_mod_zero(&s[j..(j + i)], p, &mut memo) {
                ans += 1;
            }
        }
    }

    return ans.to_string();
}

fn is_mod_zero(s: &str, p: usize, memo: &mut HashMap<String, usize>) -> bool {
    let mut s: String = String::from(s);
    if let Some(x) = memo.get(&s) {
        return x % p == 0;
    }

    while s.len() >= 20 {
        let a1: usize = *&s[0..19].parse::<usize>().unwrap();
        let m1 = a1 % p;
        s = format!("{}{}", m1, &s[19..]);
    }

    let mo = s.parse::<usize>().unwrap() % p;
    memo.insert(s, mo);
    return mo == 0;
}