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)

def main():
    n, p = map(int, input().split())
    s = input()
    mu = [None]*n
    ans = 0
    c = [0]*p
    if 10%p == 0:
        ss = map(int, s)
        ss = list(ss)
        for i in range(n):
            if ss[i]%p == 0:
                ans += i+1
        print(ans)
        return
    sr = s[::-1]
    ssr = map(int, sr)
    tens = 1
    v = 0
    for i, si in enumerate(ssr):
        v = (v + (si%p)*tens)%p
        mu[i] = v
        c[v] += 1
        tens *= 10
        tens %= p
    c[0] += 1
    for i in c:
        if i:
            ans += ((i-1)*i)//2
        
    print(ans)
    

if __name__ == "__main__":
    main()