I believe the approach just mainly boils down the simple brute force. All I am doing is ensuring $$$C - F <= \frac{A}{B} <= C+F$$$ by just switching it to $$$B(C-F) <= A <= B(C+F)$$$ and brute forcing every B. The nuances is dealing with the precision issues, which is by multiplying by some power of 10 as shown in the code below,

C, F = input().split()

i1, i2 = C.find('.'), F.find('.')

if (i1 == -1):
    i1 = len(C)
if (i2 == -1):
    i2 = len(F)

k = 1

while (i1+1 < len(C) or i2+1 < len(F)):
    if (i1+1 >= len(C)):
        C += '0'

    if (i2+1 >= len(F)):
        F += '0'

    i1 += 1
    i2 += 1
    k *= 10

C = int("".join(C.split(".")))
F = int("".join(F.split(".")))

A, B = int(1e9), int(1e9)

for i in range(1, int(1e6)):
    l, r = ((C-F)*i+k-1)//k, ((C+F)*i)//k
    l = max(1, l)
    if (r - l >= 0):
        if (l < A):
            A, B = l, i

print(A, B, sep='\n')