{-# OPTIONS_GHC -O2 -fno-cse #-}
main = do
  let m = 1000000
  putStr $ show m ++ "-th prime: "
  print $ tmawprimes !! (m - 1)
 
data A a = A a (A a) | B [a]  -- direct encoding for Split List
 
tmawprimes ::  [Int]
tmawprimes = 2:3:5:7:primes'  -- tree-merged | primes-multiples removal
   where                     --             | with 2-3-5-7 WHEEL
    primes'  = roll 11 wheel `minus` tjoin
                 [A (p*p) (B [p*q|q<-rollFrom p]) | p <- primes_]
 
    primes_  = h ++ t  `minus` tjoin
                 [A (p*p) (B [p*q|q<-rollFrom p]) | p <- primes_]
               where (h,t) = splitAt 6 (roll 11 wheel)  
 
    rollFrom n = go wheelNums wheel
      where m = (n-11) `mod` 210
            go (x:xs) (w:ws) | x==m = roll (n+w) ws 
                             | True = go xs ws
    wheelNums  = roll 0 wheel         -- [0,2,6,8,12,18, ...] 
    roll       = scanl (+)
    wheel      = 2:4:2:4:6:2:6:4:2:4:6:6:2:6:4:2:6:4:6:8:4:2:4:2:
                 4:8:6:4:6:2:4:6:2:6:6:4:2:4:6:2:6:4:2:4:2:10:2:10:wheel
 
    tjoin (a:b:c:ys) = add a (add b c) `add` tjoin (pairs ys)
     where pairs (a:b:ys)  = add a b : pairs ys
           add u@(B(x:xs)) v@(A y ys) = case compare x y of 
                                  LT -> A x (add (B xs) v)
                                  EQ -> A x (add (B xs) ys)
                                  GT -> A y (add   u    ys)
           add   (A x xs)  v          = A x (add   xs   v)
           add   (B   xs)    (B   ys) = B   (union xs   ys) 
 
    union a@(x:xs) b@(y:ys) = case compare x y of 
                                   LT -> x : union xs   b 
                                   EQ -> x : union xs   ys
                                   GT -> y : union a    ys
 
    minus a@(x:xs) b@(A y ys) = case compare x y of 
                                   LT -> x : minus xs   b
                                   EQ ->     minus xs   ys
                                   GT ->     minus a    ys

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