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: Accepted)


import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main {
    // TODO solve
    public static void main(final String[] args) {
        final Scanner scanner = new Scanner(System.in);
        final int n = scanner.nextInt();
        final int p = scanner.nextInt();
        final String s = scanner.next();
        final List<Integer> list = IntStream.range(0, n)
                .mapToObj(i -> s.charAt(i) - '0')
                .collect(Collectors.toList());

        long count = 0;
        if (p == 2 || p == 5) {
            for (int i = 0; i < list.size(); i++) {
                final int digit = list.get(i);
                if (digit % p == 0) {
                    count += i + 1;
                }
            }
        } else {
            final Map<Long, Long> counter = new HashMap<>();
            long base = 1;
            long current = 0;
            Collections.reverse(list);
            for (final int digit : list) {
                current = (current + digit * base) % p;
                base = base * 10 % p;
                if (current % p == 0) {
                    count++;
                }
                if (counter.get(current) != null) {
                    count += counter.get(current);
                }
                counter.compute(current, (k, v) -> v == null ? 1 : v + 1);
            }
        }

        System.out.println(count);
    }
}