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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

N,P = [int(i) for i in input().split()]
S = list(input())
DP = [[0]*P for i in range(N+1)]
amari =[[(a*10+num)%P for a in range(P)]for num in range(10)]#amari[num][a]
tasi = 0
if P not in[2,5]:
    for j,s in enumerate(S):
        Num = int(s)
        tasi += DP[j][0]
        for a in range(P):
            DP[j+1][amari[Num][a]] = DP[j][a]
        DP[j+1][Num%P] += 1
    print(DP[N][0] + tasi)
else:
    for j,s in enumerate(S):
        Num = int(s)
        tasi += DP[j][0]
        for a in range(P):
            DP[j+1][amari[Num][a]] += DP[j][a]
        DP[j+1][Num%P] += 1
    print(DP[N][0] + tasi)