-- helpers
binom :: Integer -> Integer -> Integer
binom n k = product [k + 1 .. n] `div` product [1 .. n - k]
binom :: Integer -> Integer -> Integer
binom n k = product [k + 1 .. n] `div` product [1 .. n - k]
binom n k = product [k + 1 .. n] `div` product [1 .. n - k]