import unittest


def change_possibilities(amount_of_money, coin_denominations):
	a= amount_of_money
	b = len(coin_denominations)
	change_coins = coin_denominations
	dp = [1]+[0]*a
	for i in range(b): 
	    for j in range(change_coins[i], a+1): dp[j]+=dp[j-change_coins[i]]
	return dp[-1]



# Tests

class Test(unittest.TestCase):

    def test_sample_input(self):
        actual = change_possibilities(4, (1, 2, 3))
        expected = 4
        self.assertEqual(actual, expected)

    def test_one_way_to_make_zero_cents(self):
        actual = change_possibilities(0, (1, 2))
        expected = 1
        self.assertEqual(actual, expected)

    def test_no_ways_if_no_coins(self):
        actual = change_possibilities(1, ())
        expected = 0
        self.assertEqual(actual, expected)

    def test_big_coin_value(self):
        actual = change_possibilities(5, (25, 50))
        expected = 0
        self.assertEqual(actual, expected)

    def test_big_target_amount(self):
        actual = change_possibilities(50, (5, 10))
        expected = 6
        self.assertEqual(actual, expected)

    def test_change_for_one_dollar(self):
        actual = change_possibilities(100, (1, 5, 10, 25, 50))
        expected = 292
        self.assertEqual(actual, expected)


unittest.main(verbosity=2)
