def make_change(amount, coins):
    """Return a list of coins that sum to amount, preferring the smallest coins
    available and placing the smallest coins first in the returned list.

    The coins argument is a dictionary with keys that are positive integer
    denominations and values that are positive integer coin counts.

    >>> make_change(2, {2: 1})
    [2]
    >>> make_change(2, {1: 2, 2: 1})
    [1, 1]
    >>> make_change(4, {1: 2, 2: 1})
    [1, 1, 2]
    >>> make_change(4, {2: 1}) == None
    True

    >>> coins = {2: 2, 3: 2, 4: 3, 5: 1}
    >>> make_change(4, coins)
    [2, 2]
    >>> make_change(8, coins)
    [2, 2, 4]
    >>> make_change(25, coins)
    [2, 3, 3, 4, 4, 4, 5]
    >>> coins[8] = 1
    >>> make_change(25, coins)
    [2, 2, 4, 4, 5, 8]
    """
    if not coins:
        return None
    smallest = min(coins)
    rest = remove_one(coins, smallest)
    "*** YOUR CODE HERE ***"

def remove_one(coins, coin):
    """Remove one coin from a dictionary of coins. Return a new dictionary,
    leaving the original dictionary coins unchanged.

    >>> coins = {2: 5, 3: 2, 6: 1}
    >>> remove_one(coins, 2) == {2: 4, 3: 2, 6: 1}
    True
    >>> remove_one(coins, 6) == {2: 5, 3: 2}
    True
    >>> coins == {2: 5, 3: 2, 6: 1} # Unchanged
    True
    """
    copy = dict(coins)
    count = copy.pop(coin) - 1
    if count:
        copy[coin] = count
    return copy

class ChangeMachine:
    """A change machine holds a certain number of coins, initially all pennies.
    The change method adds a single coin of some denomination X and returns a
    list of coins that sums to X. The machine prefers to return the smallest
    coins available. The total value in the machine never changes, and it can
    always make change for any coin (perhaps by returning the coin passed in).

    The coins attribute is a dictionary with keys that are positive integer
    denominations and values that are positive integer coin counts.

    >>> m = ChangeMachine(2)
    >>> m.coins == {1: 2}
    True
    >>> m.change(2)
    [1, 1]
    >>> m.coins == {2: 1}
    True
    >>> m.change(2)
    [2]
    >>> m.coins == {2: 1}
    True
    >>> m.change(3)
    [3]
    >>> m.coins == {2: 1}
    True

    >>> m = ChangeMachine(10) # 10 pennies
    >>> m.coins == {1: 10}
    True
    >>> m.change(5) # takes a nickel & returns 5 pennies
    [1, 1, 1, 1, 1]
    >>> m.coins == {1: 5, 5: 1} # 5 pennies & a nickel remain
    True
    >>> m.change(3)
    [1, 1, 1]
    >>> m.coins == {1: 2, 3: 1, 5: 1}
    True
    >>> m.change(2)
    [1, 1]
    >>> m.change(2) # not enough 1's remaining; return a 2
    [2]
    >>> m.coins == {2: 1, 3: 1, 5: 1}
    True
    >>> m.change(8) # cannot use the 2 to make 8, so use 3 & 5
    [3, 5]
    >>> m.coins == {2: 1, 8: 1}
    True
    >>> m.change(1) # return the penny passed in (it's the smallest)
    [1]
    >>> m.change(9) # return the 9 passed in (no change possible)
    [9]
    >>> m.coins == {2: 1, 8: 1}
    True
    >>> m.change(10)
    [2, 8]
    >>> m.coins == {10: 1}
    True

    >>> m = ChangeMachine(9)
    >>> [m.change(k) for k in [2, 2, 3]]
    [[1, 1], [1, 1], [1, 1, 1]]
    >>> m.coins == {1: 2, 2: 2, 3: 1}
    True
    >>> m.change(5) # Prefers [1, 1, 3] to [1, 2, 2] (more pennies)
    [1, 1, 3]
    >>> m.change(7)
    [2, 5]
    >>> m.coins == {2: 1, 7: 1}
    True
    """
    def __init__(self, pennies):
        self.coins = {1: pennies}

    def change(self, coin):
        """Return change for coin, removing the result from self.coins."""
        "*** YOUR CODE HERE ***"