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 Scala (2.11.7) (judge verdict: Wrong Answer)

import java.io.{BufferedOutputStream, BufferedReader, InputStreamReader, PrintWriter}

object Main {
  def main(args: Array[String]): Unit = {
    val in = new BufferedReader(new InputStreamReader(System.in))
    val out = new PrintWriter(new BufferedOutputStream(System.out))
    val Array(n, p) = in.readLine().split("\\s+").map(_.toInt)
    val s = in.readLine().toCharArray.reverse.map(_.toInt - '0')

    def getRemainders() = {
      val remainders = Array.ofDim[Int](n)

      var base = 1
      for {
        i <- s.indices
      } {
        remainders(i) = base * s(i) % p
        base = base * 10 % p
      }

      remainders
    }
    val m = getRemainders()

    def getSumOfRemainders() = {
      val sumOfRemainders = Array.ofDim[Int](n + 1)

      sumOfRemainders(0) = 0
      for {
        i <- m.indices
      } {
        sumOfRemainders(i + 1) = (sumOfRemainders(i) + m(i)) % p
      }

      sumOfRemainders
    }
    val sm = getSumOfRemainders()

    val remainders = Array.ofDim[Int](10001)
    for {
      asm <- sm
    } {
      remainders(asm) += 1
    }

    var count = 0L
    for {
      r <- remainders
      if r > 1
    } {
      count += r * (r - 1) / 2
    }

    out.println(count)
    out.flush()
  }
}