Bullseye

-- Raises a number to an Int power
(^!) :: Num a => a -> Int -> a
(^!) x n = x^n

-- Takes the integer square root
squareRoot :: Integer -> Integer
squareRoot 0 = 0
squareRoot 1 = 1
squareRoot n =
   let twopows = iterate (^!2) 2
       (lowerRoot, lowerN) =
          last $ takeWhile ((n>=) . snd) $ zip (1:twopows) twopows
       newtonStep x = div (x + div n x) 2
       iters = iterate newtonStep (squareRoot (div n lowerN) * lowerRoot)
       isRoot r  =  r^!2 <= n && n < (r+1)^!2
   in  head $ dropWhile (not . isRoot) iters


-- Maps amount of paint and inner circle radius to a ring count
circlesFromPaint :: Integer -> Integer -> Integer
circlesFromPaint p r =
    let underroot = (8*p) + (4*(r*r) - 4*r) + 1
        introot   = squareRoot underroot
        overfour  = introot - 2*r + 1
        divbyfour = div overfour 4
    in divbyfour


-- Generate strings of the format "Case #n" starting from 1
caseStrs :: [String]
caseStrs = map ((++) "Case #" . show) [1..]


-- Run the circlesFromPaint equation on a line of input
runLine :: String -> Integer
runLine line =
    let info = fmap read (words line)
        r = info !! 0
        p = info !! 1
    in circlesFromPaint p r


-- Run the program
main = do
  cases <- getLine
  contents <- getContents
  mapM_ putStrLn (zipWith (\x y -> x ++ " " ++ show y) caseStrs (map runLine (lines contents)))