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: Accepted)

use std::vec::Vec;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}

fn read_touple<T: std::str::FromStr + Copy>() -> (T, T) {
  let v: Vec<T> = read_vec();
  assert_eq!(v.len(), 2);
  (v[0], v[1])
}

fn main() {
  let (n, p) = read_touple();
  let s: Vec<usize> = read::<String>()
                        .chars()
                        .rev()
                        .map(|c| c as usize - '0' as usize)
                        .collect();

  let mut ans = 0;
  if p == 2 || p == 5 {

    for i in 0..n {
      if s[i] % p == 0 {
        ans += (n - i);
      }
    }
    println!("{}", ans);
    return
  } 

  let mut sum = vec![0; n+1];
  let mut c = 1;
  for i in 0..n {
    sum[i+1] =  sum[i] + c * s[i];
    sum[i+1] %= p;
    c *= 10;
    c %= p;
  }

  let mut count = vec![0; p];

  for i in 0..n+1 {
    let e = sum[i];
    count[e] += 1;
  } 

  for &c in &count {
    //println!("{} {}", c, (c * (c-1)) / 2);
    ans += ((c-1) * c) / 2;
  }

  //println!("{:?}", sum);
  //println!("{:?}", count);
  println!("{}", ans);
}