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.Linq;
using System.Collections.Generic;

using E = System.Linq.Enumerable;

public class Program
{
    public static void Main()
    {
        var np = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
        var n = np[0];
        var p = np[1];
        var s = Console.ReadLine().Trim();

        var k = 0L;
        if (p == 2 || p == 5)
        {
            for (int i = 0; i < s.Length; ++i)
            {
                if ((s[i] - '0') % p != 0)
                {
                    continue;
                }

                k += i + 1;
            }
        }
        else
        {
            var m = 0;
            var pow = 1;
            var bucket = new int[p];
            bucket[0] = 1;
            for (int i = 0; i < s.Length; ++i)
            {
                int ii = s.Length - i - 1;
                m += (s[ii] - '0') * pow; m %= p;
                pow *= 10; pow %= p;

                k += bucket[m]++;
            }
        }

        Console.WriteLine(k);
    }
}