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: Accepted)

import scala.io.StdIn._

object Main {
  def main(args: Array[String]): Unit = {
    solve
  }

  def solve(): Unit = {
    val input = readLine().split(" ")
    val n = input(0).toInt
    val p = input(1).toInt
    val s = readLine.toCharArray

    if (10 % p == 0) {
      var ans = 0L
      for (i <- 0 until n) {
        if ((s(i) - '0') % p == 0) {
          ans += i + 1
        }
      }
      println(ans)

    } else {
      val d = new Array[Int](n + 1)
      var ten = 1
      for (i <- n - 1 to 0 by -1) {
        val a = (s(i) - '0') * ten % p
        d(i) = (d(i + 1) + a) % p
        ten = ten * 10 % p
      }

      var ans = 0L
      val count = new Array[Long](p)
      for (i <- n to 0 by -1) {
        ans += count(d(i))
        count(d(i)) += 1
      }
      println(ans)
    }
  }
}