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: Accepted)

from collections import Counter
import sys
read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines

def main():
    N, P = map(int, readline().split())
    S = [int(i) for i in readline().strip()[::-1]]

    ans = 0
    if P == 2 or P == 5:
        for i, s in enumerate(S):
            if s % P == 0:
                ans += N - i
        
        print(ans)
        exit()

    a = [0]
    s = 0
    for i in range(N):
        s += S[i] * pow(10, i, P)
        a.append(s % P)
    
    t = Counter(a)

    ans = 0
    for v in t.values():
        ans += v * (v-1) // 2
    
    print(ans)

    


if __name__ == "__main__":
    main()