Divisible Substring

AtCoder

IDabc158_e

Time2000ms

Memory256MB

Difficulty—

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: $N$ $P$ $S$ [samples]

Samples

Input #1

4 3
3543

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 $6$.

Input #2

4 2
2020

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.

Input #3

20 11
33883322005544116655

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Divisible Substring",
    "description": {
      "content": "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 \\ti",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc158_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi has a string $S$ of length $N$ consisting of digits from `0` through `9`.\nHe loves the prime number $P$. He wants to know how many non-empty (contiguous) substrings of $S$ - there are $N \\ti...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments