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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

import itertools
n,p = [int(x) for x in input().split()]
s = input()
if p!=2 and p!=5:
  r = []
  a = int(s)
  r.append(a%p)
  for i in range(n):
    a = a-int(s[i])*10**(n-1-i)
    r.append(a%p)
  #print(r)
  r.sort()
  ans = 0
  cnt=1
  for i in range(len(r)-1):
    if r[i]==r[i+1]:
      cnt+=1
    else:
      ans +=cnt*(cnt-1)//2
      cnt=1
  print(ans+cnt*(cnt-1)//2)
elif p==2:
  ans = 0
  for i in range(n):
    if int(s[i])%2==0:
      ans +=i+1
  print(ans)
elif p==5:
  ans = 0
  for i in range(n):
    if int(s[i])%5==0:
      ans +=i+1
  print(ans)