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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;

public static class P
{
    public static void Main()
    {
        var np = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var s = Console.ReadLine();
        var p = np[1];
        var res = 0L;
        if (p == 2 || p == 5)
        {
            for (int i = 0; i < s.Length; i++)
            {
                if ((s[i] - '0') % p == 0)
                {
                    res += i + 1;
                }
            }
            Console.WriteLine(res);
            return;
        }
        var accum = new int[s.Length + 1];
        accum[accum.Length - 1] = 0;
        var pow = 1;
        for (int i = s.Length - 1; i >= 0; i--)
        {
            accum[i] = accum[i + 1] + (s[i] - '0') * pow;
            accum[i] %= p;
            pow *= 10;
            pow %= p;
        }
        foreach (var item in accum.GroupBy(x => x))
        {
            long count = item.Count();
            res += count * (count - 1) / 2;
        }
        Console.WriteLine(res);
    }
}