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: Time Limit Exceeded)

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

public class AtCoder_158_E
{
    public static void Main()
    {
        int[] line1 = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

        int n = line1[0];
        int p = line1[1];

        string s = Console.ReadLine();

        long sum = 0;
        long[] count = new long[n+1];
        Dictionary<char, int> dic = new Dictionary<char, int>()
        {
            {'0', 0} ,
            {'1', 1},
            {'2', 2},
            {'3', 3},
            {'4', 4},
            {'5', 5},
            {'6', 6},
            {'7', 7},
            {'8', 8},
            {'9', 9},
        };

        for (int i = n - 1; i >= 0; i--)
        {
            int prevAmari = 0;
            for (int j = i; j < n; j++)
            {
                prevAmari = (prevAmari * 10 + dic[s[j]]) % p;
                if (prevAmari == 0)
                {
                    count[i] = 1 + count[j+1];
                    sum += count[i];
                    break;
                }
            }
        }

        Console.WriteLine(sum);
    }
}