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.io.*;
import java.util.StringTokenizer;

public class Main {

    private static FastReader in = new FastReader(System.in);
    private static PrintWriter out = new PrintWriter(System.out);

    // private static final long MOD = (long) 1e9 + 7;

    public static void main(String[] args) {
        solve();
        out.flush();
    }

    private static void solve() {
        int n = in.nextInt();
        int q = in.nextInt();
        char[] ch = in.next().toCharArray();

        // special case
        if (q == 2 || q == 5) {
            long ans = 0;
            for (int i = 0; i < ch.length; i++) {
                int c = ch[i] - '0';
                if (c % q == 0) {
                    ans += (i + 1);
                }
            }
            out.println(ans);
            return;
        }

        int[] counts = new int[q];
        counts[0]++;
        int current = 0;
        long ans = 0;
        for (int i = ch.length - 1; i >= 0; i--) {
            int c = ch[i] - '0';
            current = add(current, c, q);

            ans += counts[current];
            counts[current]++;

            current = multiply(current, 10, q);
        }

        out.println(ans);
    }

    // a + b (mod m)
    private static int add(int a, int b, int mod) {
        return (a + b) % mod;
    }

    // a - b (mod m)
    private static int subtract(int a, int b, int mod) {
        return add(add(a, -b, mod), mod, mod);
    }

    // a * b (mod m)
    private static int multiply(int a, int b, int mod) {
        return (a * b) % mod;
    }

    // https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        FastReader(InputStream inputStream) {
            br = new BufferedReader(new
                    InputStreamReader(inputStream));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException  e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        // https://qiita.com/masakinpo/items/5f77f2a879578a85a0bb
        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }
}