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: Wrong Answer)

using System.Collections.Generic;
using System;

public class Hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        var p = int.Parse(line[1]);
        var s = Console.ReadLine().Trim();
        var a = new int[n];
        var pow = 1;
        for (int i = 0; i < n; i++)
        {
            var w = s[n - 1 - i] - '0';
            if (i != 0) pow *= 10;
            pow %= p;
            a[i] = (w * pow) % p;
        }
        getAns(n, p, a);
    }
    static void getAns(int n, int p, int[] a)
    {
        var d = new Dictionary<int, int>();
        d[0] = 1;
        var b = new int[n + 1];
        var pre = 0;
        for (int i = 0; i < n; i++)
        {
            var t = (pre + a[i]) % p;
            if (d.ContainsKey(t)) d[t]++;
            else d[t] = 1;
            pre = t;
        }
        var ans = 0L;
        foreach (var x in d)
            if (x.Value >= 2) ans += x.Value * ((long)x.Value - 1) / 2;
        Console.WriteLine(ans);
    }
}