RoundTableKnights.hs

{-# OPTIONS_GHC -O2 -optc-O3 -optc-ffast-math -cpp #-}
{-# OPTIONS_GHC -funbox-strict-fields -fexcess-precision -monly-3-regs #-}
{-# LANGUAGE BangPatterns, OverloadedStrings, ScopedTypeVariables #-}
{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE FlexibleContexts #-}

module Main where
import Control.Applicative
import Data.List
import Text.Printf
import Data.Array
import Data.Array.IO
import Data.Foldable (for_)
import Data.IORef


splitBy :: (a -> Bool) -> [a] -> [[a]]
splitBy p [] = []
splitBy p xs = a : (splitBy p $ dropWhile p $ b)
   where
     (a, b) = break p xs
 
split :: String -> [String]
split = splitBy (==' ')

divisors :: (Integral a) => a -> [a]
divisors num = divisors' num [1..num]
	where
		divisors' _ []			= []
		divisors' n (x:xs)
			| n < x * x		= []
			| n `mod` x == 0	= x:(n `div` x):divisors' n xs
			| otherwise		= divisors' n xs

yesOrNo :: Bool -> String
yesOrNo x = if x then "YES" else "NO"



f n ks = concatMap arr ds
    where 
      ds     = divisors n
      arr  x =  (filter ((>2) . length)) . (filter (all (==1))) . map  (\ y ->  (map (ar!)  $ (range ((1,y),(m,y))))) $ [1..x]
          where m = (n `div` x)
                ar = listArray ((1,1),(m , x)) $ ks 


main = do {(n:ks:_) <- map (map read) . map split . lines <$> getContents
          ; let n' =  head $ n in
            printf "%s\n" .  yesOrNo . any (not .null) $ ((f n') $ ks)
          }