Buggy python submission (verdict: Runtime Error):
import math
A, B = map(int,input().split())
if A == B:
    print(A)
else:
    LA = []
    LB = []
    for i in range(int(math.log2(A))+1):
        P = A % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LA.append(R)
    for i in range(int(math.log2(B))+1):
        P = B % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LB.append(R)
    LS = []
    def Q(a,b):
        return (a%2,b%2)
    if A == B-1:
        if Q(A,B) == (0,1):
            print(1)
        else:
            LS.append(1)
            if len(LA) == len(LB):
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            else:
                for i in range(len(LA)):
                    LS.append(1)
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
    else:
        if Q(A,B) == (0,0):
            if (B-A+1)%4 ==1:
                print(B)
            else:
                print(B+1)
        elif Q(A,B) == (0,1):
            if (B-A+1)%4 == 0:
                print(0)
            else:
                print(1)
        elif Q(A,B) == (1,0):
            if (B-A+1)%4 == 0:
                LS.append(0)
                if len(LA) > 1:
                    for i in range(1,len(LA)):
                        LS.append((LA[i]+LB[i])%2)
                if len(LB) > len(LA):
                    for i in range(len(LA),len(LB)):
                        LS.append(LB[i])
            else:
                LS.append(1)
                if len(LA) > 1:
                    for i in range(1,len(LA)):
                        LS.append((LA[i]+LB[i])%2)
                if len(LB) > len(LA):
                    for i in range(len(LA),len(LB)):
                        LS.append(LB[i])
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
        else:
            if (B-A+1)%4 == 1:
                print(A)
            else:
                print(A-1)
        

Fixed submission:
import math
A, B = map(int,input().split())
if A == 0:
    if B % 4 ==0:
        print(B)
    elif B % 4 == 1:
        print(1)
    elif B % 4 == 2:
        print(B+1)
    else:
        print(0)
elif A == B:
    print(A)
else:
    LA = []
    LB = []
    for i in range(int(math.log2(A))+1):
        P = A % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LA.append(R)
    for i in range(int(math.log2(B))+1):
        P = B % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LB.append(R)
    LS = []
    def Q(a,b):
        return (a%2,b%2)
    if A == B-1:
        if Q(A,B) == (0,1):
            print(1)
        else:
            LS.append(1)
            if len(LA) == len(LB):
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            else:
                for i in range(len(LA)):
                    LS.append(1)
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
    else:
        if Q(A,B) == (0,0):
            if (B-A+1)%4 ==1:
                print(B)
            else:
                print(B+1)
        elif Q(A,B) == (0,1):
            if (B-A+1)%4 == 0:
                print(0)
            else:
                print(1)
        elif Q(A,B) == (1,0):
            if (B-A+1)%4 == 0:
                LS.append(0)
            else:
                LS.append(1)
            if len(LA) > 1:
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            if len(LB) > len(LA):
                for i in range(len(LA),len(LB)):
                    LS.append(LB[i])
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
        else:
            if (B-A+1)%4 == 1:
                print(A)
            else:
                print(A-1)

Buggy python submission (verdict: Runtime Error):
import math
A, B = map(int,input().split())
if A == B:
    print(A)
else:
    LA = []
    LB = []
    for i in range(int(math.log2(A))+1):
        P = A % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LA.append(R)
    for i in range(int(math.log2(B))+1):
        P = B % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LB.append(R)
    LS = []
    def Q(a,b):
        return (a%2,b%2)
    if A == B-1:
        if Q(A,B) == (0,1):
            print(1)
        else:
            LS.append(1)
            if len(LA) == len(LB):
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            else:
                for i in range(1,len(LA)):
                    LS.append(LA[i])
                LS.append(LB[-1])
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
    else:
        if Q(A,B) == (0,0):
            if (B-A+1)%4 ==1:
                print(B)
            else:
                print(B+1)
        elif Q(A,B) == (0,1):
            if (B-A+1)%4 == 0:
                print(0)
            else:
                print(1)
        elif Q(A,B) == (1,0):
            if (B-A+1)%4 == 0:
                LS.append(0)
            else:
                LS.append(1)
            if len(LA) > 1:
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            if len(LB) > len(LA):
                for i in range(len(LA),len(LB)):
                    LS.append(LB[i])
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
        else:
            if (B-A+1)%4 ==1:
                print(A)
            else:
                print(A-1)

Fixed submission:
import math
A, B = map(int,input().split())
if A == 0:
    if B % 4 ==0:
        print(B)
    elif B % 4 == 1:
        print(1)
    elif B % 4 == 2:
        print(B+1)
    else:
        print(0)
elif A == B:
    print(A)
else:
    LA = []
    LB = []
    for i in range(int(math.log2(A))+1):
        P = A % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LA.append(R)
    for i in range(int(math.log2(B))+1):
        P = B % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LB.append(R)
    LS = []
    def Q(a,b):
        return (a%2,b%2)
    if A == B-1:
        if Q(A,B) == (0,1):
            print(1)
        else:
            LS.append(1)
            if len(LA) == len(LB):
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            else:
                for i in range(len(LA)):
                    LS.append(1)
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
    else:
        if Q(A,B) == (0,0):
            if (B-A+1)%4 ==1:
                print(B)
            else:
                print(B+1)
        elif Q(A,B) == (0,1):
            if (B-A+1)%4 == 0:
                print(0)
            else:
                print(1)
        elif Q(A,B) == (1,0):
            if (B-A+1)%4 == 0:
                LS.append(0)
            else:
                LS.append(1)
            if len(LA) > 1:
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            if len(LB) > len(LA):
                for i in range(len(LA),len(LB)):
                    LS.append(LB[i])
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
        else:
            if (B-A+1)%4 == 1:
                print(A)
            else:
                print(A-1)

Buggy python submission (verdict: Runtime Error):
import math
A, B = map(int,input().split())
if A == B:
    print(A)
else:
    LA = []
    LB = []
    for i in range(int(math.log2(A))+1):
        P = A % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LA.append(R)
    for i in range(int(math.log2(B))+1):
        P = B % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LB.append(R)
    LS = []
    def Q(a,b):
        return (a%2,b%2)
    if Q(A,B) == (0,0):
        LS.append(((B-A)//2)%2)
        if len(LA) > 1:
            for i in range(1,len(LA)):
                LS.append(LB[i])
        if len(LB) > len(LA):
            for i in range(len(LA),len(LB)):
                LS.append(LB[i])
    elif Q(A,B) == (0,1):
        LS.append(((B-A+1)//2)%2)
        if A == B-1:
            for i in range(1,len(LA)):
                LS.append((LA[i]+LB[i])%2)
        else:
            if len(LA) > 1:
                for i in range(1,len(LA)):
                    LS.append(0)
            if len(LB) > len(LA):
                for i in range(len(LA),len(LB)):
                    LS.append(0)
    elif Q(A,B) == (1,0):
        LS.append(((B-A+1)//2)%2)
        if A == B-1:
            if len(LA) == len(LB):
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            else:
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
                LS.append(LB[-1])
        else:
            if len(LA) > 1:
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            if len(LB) > len(LA):
                for i in range(len(LA),len(LB)):
                    LS.append(LB[i])
    else:
        LS.append(((B-A+2)//2)%2)
        if len(LA) > 1:
            for i in range(1,len(LA)):
                LS.append(LA[i])
        if len(LB) > len(LA):
            for i in range(len(LA),len(LB)):
                LS.append(0)

    ANS = 0
    for i in range(len(LS)):
        ANS += (2**i)*LS[i]

    print(ANS)

Fixed submission:
import math
A, B = map(int,input().split())
if A == 0:
    if B % 4 ==0:
        print(B)
    elif B % 4 == 1:
        print(1)
    elif B % 4 == 2:
        print(B+1)
    else:
        print(0)
elif A == B:
    print(A)
else:
    LA = []
    LB = []
    for i in range(int(math.log2(A))+1):
        P = A % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LA.append(R)
    for i in range(int(math.log2(B))+1):
        P = B % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LB.append(R)
    LS = []
    def Q(a,b):
        return (a%2,b%2)
    if A == B-1:
        if Q(A,B) == (0,1):
            print(1)
        else:
            LS.append(1)
            if len(LA) == len(LB):
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            else:
                for i in range(len(LA)):
                    LS.append(1)
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
    else:
        if Q(A,B) == (0,0):
            if (B-A+1)%4 ==1:
                print(B)
            else:
                print(B+1)
        elif Q(A,B) == (0,1):
            if (B-A+1)%4 == 0:
                print(0)
            else:
                print(1)
        elif Q(A,B) == (1,0):
            if (B-A+1)%4 == 0:
                LS.append(0)
            else:
                LS.append(1)
            if len(LA) > 1:
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            if len(LB) > len(LA):
                for i in range(len(LA),len(LB)):
                    LS.append(LB[i])
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
        else:
            if (B-A+1)%4 == 1:
                print(A)
            else:
                print(A-1)

Buggy python submission (verdict: Runtime Error):
import math
A, B = map(int,input().split())
if A == B:
    print(A)
else:
    LA = []
    LB = []
    for i in range(int(math.log2(A))+1):
        P = A % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LA.append(R)
    for i in range(int(math.log2(B))+1):
        P = B % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LB.append(R)
    LS = []
    def Q(a,b):
        return (a%2,b%2)

    if Q(A,B) == (0,0):
        LS.append(((B-A)//2)%2)
        if len(LA) > 1:
            for i in range(1,len(LA)):
                LS.append(LB[i])
            
        if len(LB) > len(LA):
            for i in range(len(LA),len(LB)):
                LS.append(LB[i])
    elif Q(A,B) == (0,1):
        LS.append(((B-A+1)//2)%2)
        if len(LA) > 1:
            for i in range(1,len(LA)):
                LS.append(0)
        if len(LB) > len(LA):
            for i in range(len(LA),len(LB)):
                LS.append(0)
    elif Q(A,B) == (1,0):
        LS.append(((B-A+1)//2)%2)
        if len(LA) > 1:
            for i in range(1,len(LA)):
                LS.append((LA[i]+LB[i])%2)
        if len(LB) > len(LA):
            for i in range(len(LA),len(LB)):
                LS.append(LB[i])
    else:
        LS.append(((B-A+2)//2)%2)
        if len(LA) > 1:
            for i in range(1,len(LA)):
                LS.append(LA[i])
        if len(LB) > len(LA):
            for i in range(len(LA),len(LB)):
                LS.append(0)

    ANS = 0
    for i in range(len(LS)):
        ANS += (2**i)*LS[i]

    print(ANS)

Fixed submission:
import math
A, B = map(int,input().split())
if A == 0:
    if B % 4 ==0:
        print(B)
    elif B % 4 == 1:
        print(1)
    elif B % 4 == 2:
        print(B+1)
    else:
        print(0)
elif A == B:
    print(A)
else:
    LA = []
    LB = []
    for i in range(int(math.log2(A))+1):
        P = A % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LA.append(R)
    for i in range(int(math.log2(B))+1):
        P = B % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LB.append(R)
    LS = []
    def Q(a,b):
        return (a%2,b%2)
    if A == B-1:
        if Q(A,B) == (0,1):
            print(1)
        else:
            LS.append(1)
            if len(LA) == len(LB):
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            else:
                for i in range(len(LA)):
                    LS.append(1)
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
    else:
        if Q(A,B) == (0,0):
            if (B-A+1)%4 ==1:
                print(B)
            else:
                print(B+1)
        elif Q(A,B) == (0,1):
            if (B-A+1)%4 == 0:
                print(0)
            else:
                print(1)
        elif Q(A,B) == (1,0):
            if (B-A+1)%4 == 0:
                LS.append(0)
            else:
                LS.append(1)
            if len(LA) > 1:
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            if len(LB) > len(LA):
                for i in range(len(LA),len(LB)):
                    LS.append(LB[i])
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
        else:
            if (B-A+1)%4 == 1:
                print(A)
            else:
                print(A-1)

Buggy python submission (verdict: Runtime Error):
import math
A, B = map(int,input().split())
LA = []
LB = []
for i in range(int(math.log2(A))+1):
    P = A % (2**(i+1))
    Q = P % (2**i)
    R = (P-Q)//(2**i)
    LA.append(R)
for i in range(int(math.log2(B))+1):
    P = B % (2**(i+1))
    Q = P % (2**i)
    R = (P-Q)//(2**i)
    LB.append(R)
LS = []
def Q(a,b):
    return (a%2,b%2)

if A == B:
    print(A)
elif Q(A,B) == (0,0):
    LS.append(((B-A)//2)%2)
    for i in range(1,len(LA)):
        LS.append(LB[i])
    if len(LB) > len(LA):
        for i in range(len(LA),len(LB)):
            LS.append(LB[i])
elif Q(A,B) == (0,1):
    LS.append(((B-A+1)//2)%2)
    for i in range(1,len(LA)):
        LS.append(0)
    if len(LB) > len(LA):
        for i in range(len(LA),len(LB)):
            LS.append(0)
elif Q(A,B) == (1,0):
    LS.append(((B-A+1)//2)%2)
    for i in range(1,len(LA)):
        LS.append((LA[i]+LB[i])%2)
    if len(LB) > len(LA):
        for i in range(len(LA),len(LB)):
            LS.append(LB[i])
else:
    LS.append(((B-A+2)//2)%2)
    for i in range(1,len(LA)):
        LS.append(LA[i])
    if len(LB) > len(LA):
        for i in range(len(LA),len(LB)):
            LS.append(0)
            
ANS = 0
for i in range(len(LS)):
    ANS += (2**i)*LS[i]
    
print(ANS)

Fixed submission:
import math
A, B = map(int,input().split())
if A == 0:
    if B % 4 ==0:
        print(B)
    elif B % 4 == 1:
        print(1)
    elif B % 4 == 2:
        print(B+1)
    else:
        print(0)
elif A == B:
    print(A)
else:
    LA = []
    LB = []
    for i in range(int(math.log2(A))+1):
        P = A % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LA.append(R)
    for i in range(int(math.log2(B))+1):
        P = B % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LB.append(R)
    LS = []
    def Q(a,b):
        return (a%2,b%2)
    if A == B-1:
        if Q(A,B) == (0,1):
            print(1)
        else:
            LS.append(1)
            if len(LA) == len(LB):
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            else:
                for i in range(len(LA)):
                    LS.append(1)
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
    else:
        if Q(A,B) == (0,0):
            if (B-A+1)%4 ==1:
                print(B)
            else:
                print(B+1)
        elif Q(A,B) == (0,1):
            if (B-A+1)%4 == 0:
                print(0)
            else:
                print(1)
        elif Q(A,B) == (1,0):
            if (B-A+1)%4 == 0:
                LS.append(0)
            else:
                LS.append(1)
            if len(LA) > 1:
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            if len(LB) > len(LA):
                for i in range(len(LA),len(LB)):
                    LS.append(LB[i])
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
        else:
            if (B-A+1)%4 == 1:
                print(A)
            else:
                print(A-1)

Buggy python submission (verdict: Runtime Error):
import math
A, B = map(int,input().split())
LA = []
LB = []
for i in range(int(math.log2(A))+1):
    P = A % (2**(i+1))
    Q = P % (2**i)
    R = (P-Q)//(2**i)
    LA.append(R)
for i in range(int(math.log2(B))+1):
    P = B % (2**(i+1))
    Q = P % (2**i)
    R = (P-Q)//(2**i)
    LB.append(R)
LS = []
def Q(a,b):
    return (a%2,b%2)
if A == B:
    print(A)
    
if Q(A,B) == (0,0):
    LS.append(((B-A)//2)%2)
    for i in range(1,len(LA)):
        LS.append(LB[i])
    if len(LB) > len(LA):
        for i in range(len(LA),len(LB)):
            LS.append(LB[i])
elif Q(A,B) == (0,1):
    LS.append(((B-A+1)//2)%2)
    for i in range(1,len(LA)):
        LS.append(0)
    if len(LB) > len(LA):
        for i in range(len(LA),len(LB)):
            LS.append(0)
elif Q(A,B) == (1,0):
    LS.append(((B-A+1)//2)%2)
    for i in range(1,len(LA)):
        LS.append((LA[i]+LB[i])%2)
    if len(LB) > len(LA):
        for i in range(len(LA),len(LB)):
            LS.append(LB[i])
else:
    LS.append(((B-A+2)//2)%2)
    for i in range(1,len(LA)):
        LS.append(LA[i])
    if len(LB) > len(LA):
        for i in range(len(LA),len(LB)):
            LS.append(0)
            
ANS = 0
for i in range(len(LS)):
    ANS += (2**i)*LS[i]
    
print(ANS)

Fixed submission:
import math
A, B = map(int,input().split())
if A == 0:
    if B % 4 ==0:
        print(B)
    elif B % 4 == 1:
        print(1)
    elif B % 4 == 2:
        print(B+1)
    else:
        print(0)
elif A == B:
    print(A)
else:
    LA = []
    LB = []
    for i in range(int(math.log2(A))+1):
        P = A % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LA.append(R)
    for i in range(int(math.log2(B))+1):
        P = B % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LB.append(R)
    LS = []
    def Q(a,b):
        return (a%2,b%2)
    if A == B-1:
        if Q(A,B) == (0,1):
            print(1)
        else:
            LS.append(1)
            if len(LA) == len(LB):
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            else:
                for i in range(len(LA)):
                    LS.append(1)
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
    else:
        if Q(A,B) == (0,0):
            if (B-A+1)%4 ==1:
                print(B)
            else:
                print(B+1)
        elif Q(A,B) == (0,1):
            if (B-A+1)%4 == 0:
                print(0)
            else:
                print(1)
        elif Q(A,B) == (1,0):
            if (B-A+1)%4 == 0:
                LS.append(0)
            else:
                LS.append(1)
            if len(LA) > 1:
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            if len(LB) > len(LA):
                for i in range(len(LA),len(LB)):
                    LS.append(LB[i])
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
        else:
            if (B-A+1)%4 == 1:
                print(A)
            else:
                print(A-1)

Buggy python submission (verdict: Runtime Error):
import math
A, B = map(int,input().split())
LA = []
LB = []
for i in range(int(math.log2(A))+1):
    P = A % (2**(i+1))
    Q = P % (2**i)
    R = (P-Q)//(2**i)
    LA.append(R)
for i in range(int(math.log2(B))+1):
    P = B % (2**(i+1))
    Q = P % (2**i)
    R = (P-Q)//(2**i)
    LB.append(R)
LS = []
def Q(a,b):
    return (a%2,b%2)
if Q(A,B) == (0,0):
    LS.append(((B-A)//2)%2)
    for i in range(1,len(LA)):
        LS.append(LB[i])
    if len(LB) > len(LA):
        for i in range(len(LA),len(LB)):
            LS.append(LB[i])
elif Q(A,B) == (0,1):
    LS.append(((B-A+1)//2)%2)
    for i in range(1,len(LA)):
        LS.append(0)
    if len(LB) > len(LA):
        for i in range(len(LA),len(LB)):
            LS.append(0)
elif Q(A,B) == (1,0):
    LS.append(((B-A+1)//2)%2)
    for i in range(1,len(LA)):
        LS.append((LA[i]+LB[i])%2)
    if len(LB) > len(LA):
        for i in range(len(LA),len(LB)):
            LS.append(LB[i])
else:
    LS.append(((B-A+2)//2)%2)
    for i in range(1,len(LA)):
        LS.append(LA[i])
    if len(LB) > len(LA):
        for i in range(len(LA),len(LB)):
            LS.append(0)
            
ANS = 0
for i in range(len(LS)):
    ANS += (2**i)*LS[i]
    
print(ANS)

Fixed submission:
import math
A, B = map(int,input().split())
if A == 0:
    if B % 4 ==0:
        print(B)
    elif B % 4 == 1:
        print(1)
    elif B % 4 == 2:
        print(B+1)
    else:
        print(0)
elif A == B:
    print(A)
else:
    LA = []
    LB = []
    for i in range(int(math.log2(A))+1):
        P = A % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LA.append(R)
    for i in range(int(math.log2(B))+1):
        P = B % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LB.append(R)
    LS = []
    def Q(a,b):
        return (a%2,b%2)
    if A == B-1:
        if Q(A,B) == (0,1):
            print(1)
        else:
            LS.append(1)
            if len(LA) == len(LB):
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            else:
                for i in range(len(LA)):
                    LS.append(1)
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
    else:
        if Q(A,B) == (0,0):
            if (B-A+1)%4 ==1:
                print(B)
            else:
                print(B+1)
        elif Q(A,B) == (0,1):
            if (B-A+1)%4 == 0:
                print(0)
            else:
                print(1)
        elif Q(A,B) == (1,0):
            if (B-A+1)%4 == 0:
                LS.append(0)
            else:
                LS.append(1)
            if len(LA) > 1:
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            if len(LB) > len(LA):
                for i in range(len(LA),len(LB)):
                    LS.append(LB[i])
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
        else:
            if (B-A+1)%4 == 1:
                print(A)
            else:
                print(A-1)

Buggy python submission (verdict: Runtime Error):
X,Y,Z,K = map(int,input().split())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
C = list(map(int,input().split()))
A.sort(reverse= True)
B.sort(reverse= True)
C.sort(reverse= True)
LIS = []
S = 0
T = 0
for s in range(X):
    for t in range(Y):
        for u in range(min((3000//(s+1)*(t+1))+1,Z))
            SU = A[s] + B[t] + C[u]
            LIS.append(SU)
LIS.sort(reverse = True)
for i in range(K):
    print(LIS[i])

Fixed submission:
import math
A, B = map(int,input().split())
if A == 0:
    if B % 4 ==0:
        print(B)
    elif B % 4 == 1:
        print(1)
    elif B % 4 == 2:
        print(B+1)
    else:
        print(0)
elif A == B:
    print(A)
else:
    LA = []
    LB = []
    for i in range(int(math.log2(A))+1):
        P = A % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LA.append(R)
    for i in range(int(math.log2(B))+1):
        P = B % (2**(i+1))
        Q = P % (2**i)
        R = (P-Q)//(2**i)
        LB.append(R)
    LS = []
    def Q(a,b):
        return (a%2,b%2)
    if A == B-1:
        if Q(A,B) == (0,1):
            print(1)
        else:
            LS.append(1)
            if len(LA) == len(LB):
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            else:
                for i in range(len(LA)):
                    LS.append(1)
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
    else:
        if Q(A,B) == (0,0):
            if (B-A+1)%4 ==1:
                print(B)
            else:
                print(B+1)
        elif Q(A,B) == (0,1):
            if (B-A+1)%4 == 0:
                print(0)
            else:
                print(1)
        elif Q(A,B) == (1,0):
            if (B-A+1)%4 == 0:
                LS.append(0)
            else:
                LS.append(1)
            if len(LA) > 1:
                for i in range(1,len(LA)):
                    LS.append((LA[i]+LB[i])%2)
            if len(LB) > len(LA):
                for i in range(len(LA),len(LB)):
                    LS.append(LB[i])
            ANS = 0
            for i in range(len(LS)):
                ANS += (2**i)*LS[i]
            print(ANS)
        else:
            if (B-A+1)%4 == 1:
                print(A)
            else:
                print(A-1)