from math import log10

​

def karatsuba(x,y):

    if x < 10 or y < 10:

        return x*y

​

    n = max(int(log10(x)+1) , int(log10(y)+1))

    n_2 = int(math.ceil(n/2.0))

    n = n if n % 2 == 0 else n + 1

​

    a, b = divmod(x, 10**n_2)

    c, d = divmod(y, 10**n_2)

​

    ac = karatsuba(a,c)

    bd = karatsuba(b,d)

​

    ad_bc = karatsuba((a+b) , (c+d)) - ac - bd

    return (((10**n)*ac) + bd + ((10**n_2) * (ad_bc)))