In his publication Liber Abaci Leonardo Bonacci, aka Fibonacci, posed a problem involving a population of idealized rabbits. These rabbits bred at a fixed rate, matured over the course of one month, had unlimited resources, and were immortal.

Beginning with one immature pair of these idealized rabbits that produce b pairs of offspring at the end of each month. Create a function that determines the number of pair of mature rabbits after n months.

To illustrate the problem, consider the following example:

```python
fib_rabbits(5, 3) returns 19
```




Month
Immature Pairs
Adult Pairs




0
1
0


1
0
1


2
3
1


3
3
4


4
12
7


5
21
19



                                
        
Hint: any Fibonacci number can be computed using the following equation Fn = F(n-1) + F(n-2)

Difficulty: EASY
Starter code: def fib_rabbits(n, b):
	

Solutions:
def fib_rabbits(n, b):
	(i, a) = (1, 0)
	for m in range(n):
		(i, a) = (a * b, a + i)
	return a


def fib_rabbits(n, b):
	(x, y) = (0, 1)
	for _ in range(n):
		(x, y) = (y, x * b + y)
	return x


def fib_rabbits(end, factor):
	(immatures, adults) = (1, 0)
	for month in range(end):
		(immatures, adults) = (factor * adults, adults + immatures)
	return adults


def fib_rabbits(n, b):
	f = [0, 1]
	for _ in range(n - 1):
		f.append(f[-1] + b * f[-2])
	return f[n]


def fib_rabbits(n, b):
	obj = {'IP': 1, 'AP': 0}
	for month in range(1, n + 1):
		cur = obj['IP']
		obj['IP'] = b * obj['AP']
		obj['AP'] += cur
	return obj['AP']


def fib_rabbits(n, b):
	table = [0 if i != 1 else 1 for i in range(0, n + 1)]
	for i in range(2, n + 1):
		table[i] = table[i - 1] + table[i - 2] * b
	return table[n]


def fib_rabbits(n, b):
	if n < 2:
		return n
	ans = [0, 1]
	for i in range(2, n + 1):
		(ans[0], ans[1]) = (ans[-1] * b, sum(ans))
	return ans[-1]


def fib_rabbits(n, b):
	f = [0] * (n + 10)
	f[1] = 1
	for i in range(2, n + 10):
		f[i] = f[i - 1] + b * f[i - 2]
	return f[n]