Problem:
Score : 300 points

Problem Statement

Given are positive integers N, M, Q, and Q quadruples of integers ( a_i , b_i , c_i , d_i ).

Consider a sequence A satisfying the following conditions:

A is a sequence of N positive integers.

1 \leq A_1 \leq A_2 \le \cdots \leq A_N \leq M.

Let us define a score of this sequence as follows:

The score is the sum of d_i over all indices i such that A_{b_i} - A_{a_i} = c_i. (If there is no such i, the score is 0.)

Find the maximum possible score of A.

Constraints

All values in input are integers.

2 ≤ N ≤ 10

1 \leq M \leq 10

1 \leq Q \leq 50

1 \leq a_i < b_i \leq N ( i = 1, 2, ..., Q )

0 \leq c_i \leq M - 1 ( i = 1, 2, ..., Q )

(a_i, b_i, c_i) \neq (a_j, b_j, c_j) (where i \neq j)

1 \leq d_i \leq 10^5 ( i = 1, 2, ..., Q )

Input

Input is given from Standard Input in the following format:

N M Q
a_1 b_1 c_1 d_1
:
a_Q b_Q c_Q d_Q

Output

Print the maximum possible score of A.

Sample Input 1

3 4 3
1 3 3 100
1 2 2 10
2 3 2 10

Sample Output 1

110

When A = \{1, 3, 4\}, its score is 110. Under these conditions, no sequence has a score greater than 110, so the answer is 110.

Sample Input 2

4 6 10
2 4 1 86568
1 4 0 90629
2 3 0 90310
3 4 1 29211
3 4 3 78537
3 4 2 8580
1 2 1 96263
1 4 2 2156
1 2 0 94325
1 4 3 94328

Sample Output 2

357500

Sample Input 3

10 10 1
1 10 9 1

Sample Output 3

1

Solution in Haskell (GHC 8.8.3) (judge verdict: Runtime Error)

-- noch nicht fertig

import qualified Data.Text as T
import qualified Data.Text.IO as T
import qualified Data.Text.Read as T
import Data.List (unfoldr)

main :: IO ()
main = do
  [n, m, q] <- map unsafeTextToInt . T.words <$> T.getLine :: IO [Int]
  let
    candidates = unfoldr next $ replicate n 1 :: [[Int]]
      where
        next :: [Int] -> Maybe ([Int], [Int])
        next = fmap <$> (,) <*> next'
          where
            next' :: [Int] -> Maybe [Int]
            next' (d : ds) | d < m     = Just $ succ d : ds
                           | otherwise = ((:) <$> head <*> id) <$> next' ds
            next' _                    = Nothing
  abcds <- sequence . replicate q $ unsafeListToTuple . map unsafeTextToInt . T.words <$> T.getLine :: IO [((Int, Int, Int), Int)]
  let
    evaluate :: [Int] -> Int
    evaluate ds = sum . map snd . filter (p . fst) $ abcds
      where
        p :: (Int, Int, Int) -> Bool
        p (x, y, z) = dy - dx == z
          where
            dy : ds' = drop (n - y) ds :: [Int]
            dx : _   = drop (pred y - x) ds' :: [Int]
  print . maximum . map evaluate $ candidates

unsafeListToTuple :: [Int] -> ((Int, Int, Int), Int)
unsafeListToTuple [w, x, y, z] = ((w, x, y), z)

unsafeTextToInt :: T.Text -> Int
unsafeTextToInt s = case T.signed T.decimal s of
  Right (n, _) -> n