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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
public class Main {
  public static void main (String args[]) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int P = sc.nextInt();
    String S = sc.next();
    long ans = 0;
    if(P==2||P==5){
      for(int i = N-1; i >= 0; i--){
        if((S.charAt(i)-'0')%P==0){
          ans+=i+1;
        }
      }
    } else {
      int amari[] = new int[P];
      int jouyo = 0;
      int kurai = 1;
      for(int i = N-1; i >= 0; i--){
        jouyo = (jouyo + (S.charAt(i)-'0')*kurai)%P;
        kurai = (kurai*10)%P;
        amari[jouyo]++;
      }
      ans = amari[0];
      for(int i = 0; i < P; i++){
        ans += amari[i]*(amari[i]-1)/2;
      }
    }
    System.out.println(ans);
    return;
  }
}