Project Euler Problem 077

primes :: [Integer]
primes = 2:f [3] [3,5..] where
  f (x:xs) ys = ps ++ f (xs++ps) [z | z<-qs,z`rem`x/=0] where
    (ps,qs) = span (< x*x) ys
ps :: [Int]
ps = map fromIntegral $ take 5000 $ primes

mulP :: Num c => [c] -> [c] -> [c]
mulP (x:xs) b = zipWith (+) (map(*x)b) $ 0:mulP xs b --母関数の積
paifold :: (Enum c, Eq a, Num a, Num c) => a -> [[c]] -> [c]
paifold nn xss = imp nn xss (1:[0,0..]) where --母関数の無限積
  imp 0 _ acc = acc
  imp _ [] acc = acc
  imp n (x:xs) acc = imp (n-1) xs (mulP acc x)

xn :: (Enum a, Num a) => Int -> [a]
xn 0 = 1:[0,0..] -- 1/(1-x^n)に相当する母関数
xn n = cycle(1:replicate (n-1) 0)

plist :: (Integer, Integer)
plist = head $ dropWhile ((<=5000).fst) $  zip lis [0..]
  where
    lis =  paifold n $ map xn ps where n = 100 --71 ok
ans1 :: Integer
ans1 = snd plist
main :: IO ()
main = print $ ans1