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 (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use itertools::Itertools;
#[allow(unused_imports)]
use num::*;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::collections::*;

fn main() {
    input! {
        n: usize, p: usize,
        s: Chars
    };

    let s = s
        .into_iter()
        .map(|ch| ch.to_digit(10).unwrap() as usize)
        .collect::<Vec<_>>();

    if p == 2 || p == 5 {
        let mut res = 0_usize;
        for i in 0..n {
            if s[i] % p == 0 {
                res += i + 1;
            }
        }
        println!("{}", res);
        return;
    }

    let mut cusum = Vec::new();
    cusum.push(0);
    let mut ten_factor = 1_usize;
    for i in (0..n).rev() {
        let x = s[i];
        let sum = (cusum.last().unwrap() + (ten_factor * x) % p) % p;
        cusum.push(sum);
        ten_factor = (ten_factor * 10) % p;
    }
    let mut map = HashMap::new();
    for s in cusum {
        *map.entry(s).or_insert(0_usize) += 1;
    }
    let mut res = 0_usize;
    for (_, c) in map {
        if c < 2 {
            continue;
        }
        res += c * (c - 1) / 2;
    }
    println!("{}", res);
}