## Problem 5: Remainder Generator Like functions, generators can also be higher-order. For this problem, we will be writing `remainders_generator`, which yields a series of generator objects. `remainders_generator` takes in an integer `m`, and yields `m` different generators. The first generator is a generator of multiples of `m`, i.e. numbers where the remainder is 0. The second is a generator of natural numbers with remainder 1 when divided by `m`. The last generator yields natural numbers with remainder `m - 1` when divided by `m`. Note that different generators should not influence each other. > Hint: Consider defining an inner generator function. Each yielded generator varies only in that the elements of each generator have a particular remainder when divided by m. What does that tell you about the argument(s) that the inner function should take in? ```python def remainders_generator(m): """ Yields m generators. The ith yielded generator yields natural numbers whose remainder is i when divided by m. >>> import types >>> [isinstance(gen, types.GeneratorType) for gen in remainders_generator(5)] [True, True, True, True, True] >>> remainders_four = remainders_generator(4) >>> for i in range(4): ... print("First 3 natural numbers with remainder {0} when divided by 4:".format(i)) ... gen = next(remainders_four) ... for _ in range(3): ... print(next(gen)) First 3 natural numbers with remainder 0 when divided by 4: 4 8 12 First 3 natural numbers with remainder 1 when divided by 4: 1 5 9 First 3 natural numbers with remainder 2 when divided by 4: 2 6 10 First 3 natural numbers with remainder 3 when divided by 4: 3 7 11 """ "*** YOUR CODE HERE ***" ``` Note that if you have implemented this correctly, each of the generators yielded by `remainder_generator` will be infinite - you can keep calling next on them forever without running into a `StopIteration` exception.

Here is one possible solution to the problem:

def remainders_generator(m):
    def generator(i):
        while True:
            yield i
            i += m
    return (generator(i) for i in range(m))

# Example usage:
gen = remainders_generator(4)
for i in range(4):
    print("First 3 natural numbers with remainder {0} when divided by 4:".format(i))
    g = next(gen)
    for _ in range(3):
        print(next(g))

The `remainders_generator` function returns a generator expression that creates `m` generators, one for each remainder value. The inner `generator` function takes an initial value `i` and yields it, then increments it by `m` and yields again, and so on, forever. This ensures that the generator produces an infinite stream of natural numbers with the desired remainder value.

In the example usage, we create a `remainders_generator` object with `m=4`, and then for each remainder value `i` from 0 to 3, we get the corresponding generator and print the first 3 numbers it yields. The output should be:

First 3 natural numbers with remainder 0 when divided by 4:
0
4
8
First 3 natural numbers with remainder 1 when divided by 4:
1
5
9
First 3 natural numbers with remainder 2 when divided by 4:
2
6
10
First 3 natural numbers with remainder 3 when divided by 4:
3
7
11