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.Diagnostics;
using System.Linq;
using System.Numerics;

internal static class CR
{
    public static string GetText() { return Console.ReadLine(); }
    public static List<string> GetTexts() { return Console.ReadLine().Split(' ').ToList(); }
    public static long GetLong() { return long.Parse(Console.ReadLine()); }
    public static List<long> GetLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }
}

namespace AtCoder.E
{
    public class Program
    {
        public static long N { get; private set; }
        public static long P { get; private set; }
        public static string S { get; private set; }

        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var inputs = CR.GetLongs();
            N = inputs[0];
            P = inputs[1];
            S = CR.GetText();

            var sLength = S.Length;
            var count = 0;
            for (int i = 0; i < sLength; i++)
            {
                for (int j = i + 1; j < sLength + 1; j++)
                {
                    var array = S.Substring(i, j - i).SkipWhile(x => x == '0').ToArray();
                    if (array.Length == 0)
                    {
                        count++;
                        continue;
                    }

                    var n = BigInteger.Parse(new string(array));
                    if (n % P == 0)
                    {
                        count++;
                    }
                }
            }

            return count;
        }
    }
}