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 PHP7 (7.0.15) (judge verdict: Runtime Error)

<?php
$a = fgets(STDIN);
$array = explode(' ', $a);
$n = str_replace("\n", '', $array[0]);
$p = str_replace("\n", '', $array[1]);
$str = str_replace("\n", '', fgets(STDIN));
for($i = 0; $i < $n; $i++) {
  $num_arr[] = $str[$i];
  $tmp_str = $str[$i];
  $t = 1;
  while($t < $n-$i) {
    $tmp_str .= $str[$i + $t];
    $num_arr[] = $tmp_str;
    $t++;
  }
}

$result = 0;
foreach($num_arr as $val) {
  if($val % $p == 0) {
    $result++;
  }
}
echo $result;
?>