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 (a*i**2+b*i+c)/m
def T(n,a,b,c,m):
    S = 0
    for i in range(1,n+1):
        S += f(a,b,c,m,i)
    return S
a, b, c, m = np.random.randint(1,11,4)
n = 10
print(n)
print('{0} * i^2 + {1} * i + {2} / {3}'.format(a,b,c,m))
print('sum from 1 to n', T(n,a,b,c,m))
def U(n,a,b,c,m):
    S = 0
    for i in range(1,n+1):
        j = i
        if i%2==0:
            j = i//2
            S += f(a,b,c,m,j)
            if j!=i:
                S