from functools import cache

@cache
def solve(n, k):
    if n <= 0:
        return [[]]
    elif n == 1:
        return [[1]]
    m = 1
    ans = []
    while m**k <= n:
        r = n - m**k
        for xs in solve(r, k):
            if (len(xs) > 0 and xs[-1] <= m) or len(xs) == 0:
                ans.append(xs[:] + [m])
        m += 1
    return ans

def waring(n, k):
    s = solve(n, k)
    l = min(len(xs) for xs in s)
    return [x for x in s if len(x) == l]
sol = waring(54, 4)
print(sol)