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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#![allow(unused_imports)]
use proconio::input;
use proconio::marker::*;

use comp::binary_search;
use std::collections::BTreeMap;

fn build_acc(nn: &Vec<i32>, p: i32) -> Vec<i32> {
    let n = nn.len();
    let mut tmp = vec![0; n + 1];
    let mut mul = 1;

    for i in 0..n {
        let i = n - i;
        tmp[i - 1] = tmp[i] + (nn[i - 1] * mul);
        tmp[i - 1] %= p;
        mul *= 10;
        mul %= p;
    }
    tmp
}

#[test]
fn test_build_acc() {
    let nn = vec![1, 2, 3];
    assert_eq!(build_acc(&nn, 3), vec![0, 2, 0, 0]);

    let nn = vec![4, 2, 3];
    assert_eq!(build_acc(&nn, 3), vec![0, 2, 0, 0]);
    let nn = vec![8, 5, 9];
    assert_eq!(build_acc(&nn, 2), vec![1, 1, 1, 0]);
    let nn = vec![9, 8, 9, 2];
    assert_eq!(build_acc(&nn, 2), vec![0, 1, 1, 0, 0]);
}

fn main() {
    input!(n: usize, p: i32, cc: Chars);
    let nn: Vec<i32> = cc
        .iter()
        .map(|c| c.to_digit(10).unwrap() as i32 % p)
        .collect();

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

    let acc = build_acc(&nn, p);
    let mut counters: BTreeMap<i32, usize> = BTreeMap::new();
    for (_, &v) in acc.iter().enumerate() {
        *counters.entry(v).or_default() += 1;
    }
    let mut cnt = 0;
    for (_, &v) in counters.iter() {
        cnt += (v * (v - 1)) / 2;
    }

    println!("{}", cnt);
}
*/

fn main() {
    let exe = "/tmp/bin22A15A86";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";