#Rules of the game: Do not use python built-in integer arithmetic 
# (its ok to add a constant number of bits though) 



def Intify(L):    # This converts a 0/1-list in a Python integer  
    s = 0         # We use this for checking correctness of our algorithms 
    M = 1
    
    for j in L:
        if (j != 0):
            s = s+ M
        M = M*2 
    return s
                    
def Add(L1,L2):
    
    if (len(L1) <  len(L2)):
        L1, L2 = L2, L1  #swaps the pointers to the two lists     
            
    Out = []
    carry = 0

    for i in range(len(L1)):
        if (i < len(L2)):
            h = carry + L1[i] + L2[i]
        else:
            h = carry + L1[i]
        
        Out.append(h%2)
        
        if h > 1:
            carry = 1
        else:
            carry = 0                     
    
    if carry == 1:
        Out.append(1)
    return Out 

def Leading1(L):
    s = -1
    for i in range(len(L)):
        if L[i] != 0:
            s = i
    return s

def Multiply(L1,L2):    #condition L2 does not represent 0
    if Leading1(L2) == -1:
        return [0]
    else:
        H =list(L2)
        b = H.pop(0)
        Z = Multiply(L1,H)
        Z.insert(0,0)
        if b == 0:
            return Z
        else:
            return Add(Z,L1)
        
    
    


L1 = [1,0,1]

print L1 , Intify(L1), "\n"

L2 = [1, 1,1,1,0,1]

print L2 , Intify(L2), "\n"

L3 = Add(L1,L2)

print L3 , Intify(L3), "\n"

print "L1 * L2", Intify(Multiply(L1,L2)), Multiply(L1,L2)