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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program divisible_substring
  implicit none
  integer :: n, p, i, m, d = 0, k, l
  character(200000) :: s
  integer(8) :: cnt(0:10000) = 0, ans = 0
  read(*,*) n, p
  read(*,*) s
  k = inv(10)
  do i = 1, n
    m = mod(ichar(s(i:i))-48,p)
    l = mod(d+m,p)
    cnt(l) = cnt(l)+1
    d = modulo(d-m*k,p)
    ans = ans+cnt(d)
  end do
  write(*,'(i0)') ans
contains
  function inv(n) result(y)
    integer, intent(in) :: n
    integer :: a, b, x, y, t, q
    a = modulo(n,p)
    b = p
    x = 0
    y = 1
    do while (b /= 0)
      q = a/b
      t = b
      b = mod(a,b)
      a = t
      t = y
      y = x
      x = t-q*x
    end do
    y = modulo(y,p)
  end
end program divisible_substring