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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;
using static System.Math;
using static Math2;
using static io;


class Program
{
    static void Main(string[] args)
    {
        var wrong_answer = new wrong_answer();
        wrong_answer.Solve();
    }
}

public class wrong_answer
{
    const int INF = 1 << 29;
    const long INFL = 1L << 60;
    const int MOD = 1000000007;
    const int MOD2 = 998244353;



    public void Solve()
    {
        var o = intm;
        var n = o[0];
        var p = o[1];
        var s = str;

        var ans2 = 0;
        if (p == 2 || p == 5)
        {

            for (int i = 0; i < n; ++i)
            {
                if ((s[i] - '0') % p == 0)
                {
                    ans2 += n - i;
                }
            }
            write(ans2);
            return;
        }

        var r = new int[p];
        var sum = 0;
        var p10 = 0;
        r[0]++;
        for (int i = 0; i < n; ++i)
        {
            sum = sum + (s[n - i - 1] - '0') * pow(10, p10, p);
            p10++;
            sum %= p;
            r[sum]++;
        }
        var ans = 0;
        for (int i = 0; i < p; ++i)
        {
            ans += r[i] * (r[i] - 1) / 2;
        }
        write(ans);
    }

}



public static class Math2
{
    public static long pow(long i, long n, long MOD = 1000000007)
    {
        long res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            n >>= 1;
        }
        return res;
    }
    public static int pow(int i, int n, int MOD = 1000000007)
    {
        int res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            n >>= 1;
        }
        return res;
    }

    public static long gcd(long i, long y)
    {
        while (y != 0)
        {
            var r = i % y;
            i = y;
            y = r;
        }
        return i;
    }

    public static long lcm(long i, long y)
    {
        return i * y / gcd(i, y);
    }

    public static BigInteger bgcd(BigInteger i, BigInteger y)
    {
        while (y != 0)
        {
            var r = i % y;
            i = y;
            y = r;
        }
        return i;
    }

    public static BigInteger blcm(BigInteger i, BigInteger y)
    {
        return i * y / bgcd(i, y);
    }

    public static Dictionary<long, int> primefactorization(long N)
    {

        var ret = new Dictionary<long, int>();

        for (long i = 2; i * i <= N; ++i)
        {
            int cnt = 0;
            while (N % i == 0)
            {
                cnt++;
                N /= i;
            }
            if (cnt != 0) ret[i] = cnt;

        }
        if (N >= 2) ret[N] = 1;

        return ret;

    }

    public static List<long> divisorenumrate(long N)
    {
        var ret = new List<long>();

        for (long i = 1; i * i <= N; ++i)
        {

            if (N % i == 0)
            {
                ret.Add(i);
                ret.Add(N / i);
            }

        }

        return ret;

    }

    public static void swap<T>(ref T a, ref T b)
    {
        var i = a;
        a = b;
        b = i;
    }
    public static void chmin<T>(ref T a, T b) where T : IComparable
    {
        if (a.CompareTo(b) > 0) a = b;
    }
    public static void chmax<T>(ref T a, T b) where T : IComparable
    {
        if (a.CompareTo(b) < 0) a = b;
    }

}

public static class io
{
    //in
    public static string str => Console.ReadLine();

    public static string[] strm => str.Split(' ');

    public static long[] longm => strm.Select(long.Parse).ToArray();
    public static int[] intm => strm.Select(int.Parse).ToArray();
    public static char[] charm => str.ToArray();
    public static double[] doublem => strm.Select(double.Parse).ToArray();
    public static long long1 => longm[0];
    public static int int1 => intm[0];
    public static char char1 => charm[0];
    public static double double1 => doublem[0];
    public static void write(string a) => Console.WriteLine(a);
    public static void write(params object[] i) => write(string.Join(" ", i));
    public static void write<T>(IEnumerable<T> a) => write(string.Join(" ", a));
    public static void yn(bool i) { if (i) write("Yes"); else write("No"); }

}