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: Wrong Answer)

import java.util.*;
import java.util.stream.Collectors;
import java.io.*;
import java.math.BigDecimal;
import java.nio.charset.StandardCharsets;

public class Main {
	int N, P;
	String S;
	List<BigDecimal> vals;
	long result = 0;
	Map<BigDecimal, List<Integer>> map;

	public static void main(String[] args) throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);
		Main ins = new Main(in);
		ins.calc();
		ins.showResult();
	}

	Main(BufferedReader in) throws IOException {
		String[] tokens = in.readLine().split(" ");
		N = Integer.parseInt(tokens[0]);
		P = Integer.parseInt(tokens[1]);
		S = in.readLine();
		this.map = new HashMap<>();
		// 初期化
		BigDecimal zero = new BigDecimal(0);
		this.map.put(zero, new ArrayList<Integer>());
		map.get(zero).add(S.length());
		BigDecimal p = new BigDecimal(P);
		StringBuilder strBuilder = new StringBuilder();
		for (int i = 0; i < S.length(); ++i) {
			strBuilder.append(S.charAt(i));
			BigDecimal val = new BigDecimal(strBuilder.toString());
			BigDecimal mod = val.remainder(p);
			if (!map.containsKey(mod)) {
				map.put(mod, new ArrayList<Integer>());
			}
			map.get(mod).add(i);
		}
	}

	void calc() {
		if (P != 2 && P != 5) {
			for (BigDecimal mod : map.keySet()) {
				int listSize = map.get(mod).size();
				if (listSize <= 1) {
					// 何もしない
				} else if (listSize == 2) {
					result += 1;
				} else {
					result += (listSize) * (listSize - 1) / 2;
				}
			}
		} else {
			// 右端だけ見ればよい
			for (int i = 0; i < S.length(); ++i) {
				Integer val = Integer.parseInt(S.substring(i, i + 1));
				if (val % P == 0) {
					// i+1をresultに足す
					result += i + 1;
				}
			}
		}
	}

	void showResult() {
		System.out.println(result);
	}

}