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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Data.List
import qualified Data.Sequence as Seq
import Data.Foldable

mapOverTail :: ([a] -> b) -> [a] -> [b]
mapOverTail _ [] = []
mapOverTail f xs = (f xs):mapOverTail f (tail xs)

accumulate :: (Int, Int, Int) -> Int -> (Int, Int, Int)
accumulate (prevN, prime, sum) n = (modRes, prime, (if modRes == 0 then 1 else 0) + sum)
  where modRes = (prevN * 10 + n) `mod` prime

third :: (a, a, a) -> a
third (_, _, x) = x

main :: IO ()
main = do
  line <- getLine
  let (_:p:_) = (map (read :: String -> Int) . words) line
  str <- getLine
  let numStr = map (\x -> read [x] :: Int) str
  let noOfDivisibles = sum $ map third $ mapOverTail (foldl accumulate (0, p, 0)) numStr
  putStrLn $ show noOfDivisibles