1. Define f(a, b, c, m, i) = Floor[(a*i^2+b*i+c)/m]. 2. define a function T to find S = Sum[f(a, b, c, m, i), {i, 1, n}]. 3. define the values of a, b, c, and m randomly as positive integers less than or equal to 10. 4. for n=10^j with j=1, if the running time of T exceeds log(n) for function T with natural number n, derive an algorithm whose running time does not exceed log(n) for n=10^j, and define a new function U that optimizes function T using this algorithm. 5. compute and output S using U.

def f(a, b, c, m, i):
  return math.floor((a*i**2+b*i+c)/m)
  
def T(n):
  S = 1
  for i in range(1, n):
    S += f(a, b, c, m, i)
  return S

a = random.randint(1, 10)
b = random.randint(1, 10)
c = random.randint(1, 10)
m = random.randint(1, 10)

j = 1
while True:
  n = 10 ** j
  if T(n) > math.log(n):
    print("j = %d, n = %d, T(n) > log(n)" %(j, n))
    break
  j += 1