Chain of powers X75997

You have to program the function @short_power7_chains@ below. Remember that 1 is a power of 7: $7^0 = 1$. The following auxiliar function may be helpful.

def is_power7(n):
    '''
    Requires a non negative integer n.
    Returns True when n is a power of 7
    Returns False when n is not a power of 7
    '''
    if n == 0:
        return False
    while n != 1:
        if n%7 != 0:
            return False
        n = n//7
    return True

• Write a function @short_power7_chains(f, k)@ that given a list $f$ of non negative integers and an integer $k$ greater than zero returns True when all the chains formed by powers of seven have size at most $k$; otherwise the function returns False. A chain of powers of seven is a block of consecutive numbers in the list all of them being a power of seven.

Scoring

The function counts 100 points.

Sample session