Money exchange solver in Haskell - very slow naive version

countExchanges :: (Integral a) => a -> [a] -> a
countExchanges sum coins
    | sum == 0 = 1
    | sum < 0 || null coins = 0
    | otherwise = countExchanges (sum - head coins) coins +
                  countExchanges sum (tail coins)

main = print (countExchanges 100 [50, 25, 10, 5, 1])