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: Runtime Error)

import java.util.Arrays;
import java.util.Scanner;

class Main{
	static long N,P;
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		//DPっぽい
		N=sc.nextLong();
		P=sc.nextLong();
		String s=sc.next();
		long[][] renDP = new long[(int)N][(int)P];		//剰余のテーブル
		long cut= 0;
		for(int i=0; i<N; i++) {
			Arrays.fill(renDP[i],0);
		}
		renDP[0][(s.charAt(0)-'0')% ((int)P)] ++;
		if(N == 1) {
			//
		}
		else {
			for(int i=1; i<N; i++) {
				int num = s.charAt(i)-'0';
				for(int j=0; j<P; j++) {
					renDP[i][((int)((j*10 + num)% P))] += renDP[i-1][j];
					if(j  == 0) {
						cut +=renDP[i-1][j];
					}
				}
				renDP[i][(int)(num % P)]++;
			}
		}
		pl(renDP[(int)N-1][0] + cut);
		//output(renDP);
		//output(cutDP);
	}
	public static void pl(Object o) {
		System.out.println(o);
	}public static void p(Object o) {
		System.out.print(o);
	}
	/*public static void output(long[][] a) {
		for(int j=0; j<P; j++) {
			for(int i = 0 ; i < N ; i++) {
				p(a[i][j]+" ");
			}
			pl(a[N][j]);
		}
	}*/
}