101584: [AtCoder]ABC158 E - Divisible Substring

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