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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

public class AtCoderE
{
    static void Main()
    {
        int n;
        int p;
        {
            var line = Console.ReadLine();
            var words = line.Split(' ');
            n = int.Parse(words[0]);
            p = int.Parse(words[1]);
        }
        string s = Console.ReadLine();
        char[] array = s.ToArray();

        if (10 % p == 0)
        {
            long ans = 0;
            for (int i = 0; i < n; i++)
            {
                int num = int.Parse(array[i].ToString());
                if (num % p == 0)
                {
                    ans += i + 1;
                }
            }
            Console.WriteLine(ans);
            return;
        }

        int[] modSum = new int[n + 1];
        int tenMod = 1;
        for (int i = n - 1; i >= 0; i--)
        {
            int num = int.Parse(array[i].ToString());
            modSum[i] = ((num * tenMod % p) + modSum[i + 1]) % p;
            tenMod = (tenMod * 10) % p;
        }

        long answer = 0;
        int[] counts = new int[p];
        for (int i = 0; i <= n; i++)
        {
            answer += counts[modSum[i]];
            counts[modSum[i]]++;
        }

        Console.WriteLine(answer);
    }
}