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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.math.BigInteger;
import java.util.Scanner;

public class Main
{
	public static void main(String[] args)
	{
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int p = scan.nextInt();
		String s = scan.next();
		scan.close();

		char[] c = s.toCharArray();
		int[] k = new int[200000];

		for (int i=0; i<n; i++) {
			k[i] = c[i] - 48;
		}
		int ans = 0;
		BigInteger bp = BigInteger.valueOf(p);
		for (int i=0; i<n; i++) {
			for (int j=i; j<n; j++) {
				if (num(i,j,k).mod(bp).equals(BigInteger.ZERO)) ans++;
			}
		}

		System.out.println(ans);
	}
	static BigInteger num(int start, int end, int[] k) {
		BigInteger ans = BigInteger.valueOf(k[start]);
		for (int i=start+1; i<=end; i++) {
			ans = ans.multiply(BigInteger.TEN).add(BigInteger.valueOf(k[i]));
		}
		return ans;
	}
}