Problem:
 Score : 400 points    Problem Statement Let f(A, B) be the exclusive OR of A, A+1, ..., B . Find f(A, B) .   What is exclusive OR?  The bitwise exclusive OR of integers c_1, c_2, ..., c_n (let us call it y ) is defined as follows:   When y is written in base two, the digit in the 2^k 's place ( k \geq 0 ) is 1 if, the number of integers among c_1, c_2, ...c_m whose binary representations have 1 in the 2^k 's place, is odd, and 0 if that count is even.   For example, the exclusive OR of 3 and 5 is 6 . (When written in base two: the exclusive OR of 011 and 101 is 110 .)

Solution (Python):
a,b=map(int,input().split())

def calc(x):
      
    a = x%4

    if a == 0:
        return x
    elif a == 1:
        return 1
    elif a == 2:
       return x|1
    else:
        return 0
 
print(calc(b) ^ calc(a-1))

Solution (Python):
a,b=map(int,input().split())

def calc(x):
      
    a = x%4

    if a == 0:
        return x
    elif a == 1:
        return 1
    elif a == 2:
       return x^1
    else:
        return 0
 
print(calc(b) ^ calc(a-1))

Solution (Python):






import sys
input = sys.stdin.readline

import math

import bisect
from collections import defaultdict
from collections import deque
from functools import lru_cache






MOD = 10**9+7
INF = float('inf')






def I(): return int(input().strip())
def S(): return input().strip()
def IL(): return list(map(int,input().split()))
def SL(): return list(map(str,input().split()))
def ILs(n): return list(int(input()) for _ in range(n))
def SLs(n): return list(input().strip() for _ in range(n))
def ILL(n): return [list(map(int, input().split())) for _ in range(n)]
def SLL(n): return [list(map(str, input().split())) for _ in range(n)]


def P(arg): print(arg); return
def Y(): print("Yes"); return
def N(): print("No"); return
def E(): exit()
def PE(arg): print(arg); exit()
def YE(): print("Yes"); exit()
def NE(): print("No"); exit()


def DD(arg): return defaultdict(arg)



def inv(n): return pow(n, MOD-2, MOD)


kaijo_memo = []
def kaijo(n):
  if(len(kaijo_memo) > n):
    return kaijo_memo[n]
  if(len(kaijo_memo) == 0):
    kaijo_memo.append(1)
  while(len(kaijo_memo) <= n):
    kaijo_memo.append(kaijo_memo[-1] * len(kaijo_memo) % MOD)
  return kaijo_memo[n]

gyaku_kaijo_memo = []
def gyaku_kaijo(n):
  if(len(gyaku_kaijo_memo) > n):
    return gyaku_kaijo_memo[n]
  if(len(gyaku_kaijo_memo) == 0):
    gyaku_kaijo_memo.append(1)
  while(len(gyaku_kaijo_memo) <= n):
    gyaku_kaijo_memo.append(gyaku_kaijo_memo[-1] * pow(len(gyaku_kaijo_memo),MOD-2,MOD) % MOD)
  return gyaku_kaijo_memo[n]

def nCr(n,r):
  if(n == r):
    return 1
  if(n < r or r < 0):
    return 0
  ret = 1
  ret = ret * kaijo(n) % MOD
  ret = ret * gyaku_kaijo(r) % MOD
  ret = ret * gyaku_kaijo(n-r) % MOD
  return ret


def factorization(n):
  arr = []
  temp = n
  for i in range(2, int(-(-n**0.5//1))+1):
    if temp%i==0:
      cnt=0
      while temp%i==0: 
        cnt+=1 
        temp //= i
      arr.append([i, cnt])
  if temp!=1:
    arr.append([temp, 1])
  if arr==[]:
    arr.append([n, 1])
  return arr


def make_divisors(n):
  divisors = []
  for i in range(1, int(n**0.5)+1):
    if n % i == 0:
      divisors.append(i)
      if i != n // i: 
        divisors.append(n//i)
  return divisors


def gcd(a, b):
    while b:
        a, b = b, a % b
    return a


def lcm(a, b):
    return a * b // gcd (a, b)


def count_bit(n):
  count = 0
  while n:
    n &= n -1
    count += 1
  return count


def base_10_to_n(X, n):
  if X//n:
    return base_10_to_n(X//n, n)+[X%n]
  return [X%n]

def base_n_to_10(X, n):
  return sum(int(str(X)[-i-1])*n**i for i in range(len(str(X))))


def int_log(n, a):
  count = 0
  while n>=a:
    n //= a
    count += 1
  return count





A,B = IL()

def xor(N):
  ret = int((N%4 == 1 or N%4 == 2))
  n = int_log(N,2)
  for i in range(1,n+1)[::-1]:
    if N >= (1<<i):
      ret += (1<<i) * (1-N%2)
      N -= (1<<i)
  return ret

print(xor(B)^xor(A-1))

Solution (Python):
def Z(): return int(input())
def ZZ(): return [int(_) for _ in input().split()]

MAX_L = 43

def main():
    A, B = ZZ()

    p = []
    e = 1
    for _ in range(MAX_L+1):
        p.append(e)
        e *= 2

    def bitc(num):
        ret = []
        for i in range(1, MAX_L+1):
            x = (num//p[i]) * p[i-1] + max(0, num%p[i]-p[i-1]+1)
            ret.append(x%2)
        return ret

    a = bitc(max(0, A-1))
    b = bitc(B)
    output = 0
    for i in range(MAX_L): output += (a[i]+b[i])%2 * p[i]
    print(output)

    return

if __name__ == '__main__':
    main()

Solution (Python):
A, B = map(int, input().split())
def f(x):
    chk = x % 4
    if chk == 0:
        return x
    if chk == 1:
        return 1
    if chk == 2:
        return x + 1
    if chk == 3:
        return 0

if A != 0:
    A -= 1
print(f(A) ^ f(B))

Solution (Python):
a, b = map(int, input().split())
def f(x):
    if (x + 1) % 4 == 0:
        return 0
    elif (x + 1) % 4 == 1:
        return x
    elif (x + 1) % 4 == 2:
        return x ^ (x - 1)
    else:
        return x ^ (x - 1) ^ (x - 2)
print(f(b) ^ f(a - 1))

Solution (Python):
A,B=map(int,input().split())

def calc_xor(n): 
  if n%2==0:
    p=n//2
    if p%2==0:
      q=0
    else:
      q=1
    return q^n
  else:
    p=(n+1)//2
    if p%2==0:
      q=0
    else:
      q=1
    return q



print(calc_xor(A-1)^calc_xor(B))

Solution (Python):
A,B = map(int,input().split())
b = list(bin(B))[2:]
b.reverse()
if A%2 == 0:
    if ((B-A)+1)%2 == 0:
        if ((B-A)+1)//2%2 == 0:
            print(0)
        else:
            print(1)
    else:
        if ((B-A)+1)//2%2 == 0:
            print(B)
        else:
            if b[0] == '0':
                print(B+1)
            else:
                print(B-1)
else:
    if ((B-A)+1)%2 == 0:
        if ((B-A)+1)//2%2 == 1:
            print(A^B)
        else:
            print(1^A^B)
    else:
        if ((B-A)+1)//2%2 == 0:
            print(A)
        else:
            print(A^1)

Solution (Python):
a, b = map(int, input().split())
if a % 2 == 0:
  if b % 2 == 0:
    if (b-a)//2%2 == 0:
      print(b)
    else:
      print(b^1)
  else:
    if (b-a+1)//2%2 == 0:
      print(0)
    else:
      print(1)
else:
  if b % 2 == 0:
    if (b-1-a)//2%2 == 0:
      print(a^b)
    else:
      print(a^b^1)
  else:
    if (b-a)//2%2 == 0:
      print(a)
    else:
      print(a^1)

Solution (Python):
a,b=map(int,input().split())
if a%2==0:
    if b%2==0:
        use=((b-a)//2)%2
        print(use^b) 
    else:
        use=((b-a+1)//2)%2
        print(use)
else:
    temp=a 
    a+=1
    if b%2==0:
        use=((b-a)//2)%2
        print(temp^use^b) 
    else:
        use=((b-a+1)//2)%2
        print(temp^use)

Solution (Python):
A, B = map(int, input().split())
A -= 1
if A % 2 == 1:
    if (A // 2 + 1) % 2 == 1:
        A = 1
    else:
        A = 0
else:
    if (A // 2) % 2 == 1:
        A = 1 ^ A
    else:
        A = 0 ^ A
if B % 2 == 1:
    if (B // 2 + 1) % 2 == 1:
        B = 1
    else:
        B = 0
else:
    if (B // 2) % 2 == 1:
        B = 1 ^ B
    else:
        B = 0 ^ B

print(A^B)

Solution (Python):
A, B = map(int, input().split())
A -= 1
ak, amod = divmod(A, 4)

cum_a = 0
if amod == 0:
    cum_a = A
elif amod == 1:
    cum_a = 1
elif amod == 2:
    cum_a = 4*ak + 3
else:
    cum_a = 0

bk, bmod = divmod(B, 4)
cum_b = 0
if bmod == 0:
    cum_b = B
elif bmod == 1:
    cum_b = 1
elif bmod == 2:
    cum_b = 4*bk + 3
else:
    cum_b = 0

print(cum_a ^ cum_b)

Solution (Python):
def xor_sum(a):
    if a == 0 or a == 1:
        return a
    elif a == 2:
        return 3
    elif a == 3:
        return 0
    else:
        b = bin(a)[2:]
        if a % 2 == 0:
            return 2**(len(b)-1) + xor_sum(a % 2**(len(b)-1))
        else:
            return xor_sum(a % 2**(len(b)-1))

def main():
    A,B = map(int,input().split())

    a,b = xor_sum(max(0,A-1)),xor_sum(B)
    print(a ^ b)

if __name__ == "__main__":
    main()

Solution (Python):
A, B = map(int, input().split())
A -= 1


def calc(n):
    if n % 2 == 1:
        if (n + 1) % 4 == 0:
            return 0
        else:
            return 1
    else:
        return calc(n-1) ^ n


print(calc(B) ^ calc(A))

Solution (Python):
def solve():
    A, B = map(int,input().split())
    A_res = func(max(A-1,0))
    B_res = func(B)
    ans = 0
    two_factor = 1
    for i in range(60):
        if not A_res[i] == B_res[i]:
            ans += two_factor
        two_factor *= 2
    
    print(ans)

def func(N):
    res = [0] * 60
    for i in range(60):
        if i == 0 and not (N % 4 == 0 or N % 4 == 3):
            res[i] = 1
        elif N & (1<<i):
            if (N+1) % 2 != 0:
                res[i] = 1

    return res

if __name__ == '__main__':
    solve()

Solution (Python):
a,b=map(int,input().split())
lenb=len(str(bin(b)))-2















result=""

if a!=0:
    a-=1
if a%4 in [1,2]:
    a4="1"
else:
    a4="0"
if b%4 in [1,2]:
    b4="1"
else:
    b4="0"

if a4==b4:
    result="0"
else:
    result="1"

for i in range(1,lenb):
    a4=(max(0,(a+1)%(2**(i+1))-(2**(i))))%2
    b4=(max(0,(b+1)%(2**(i+1))-(2**(i))))%2
    if a4==b4:
        result="0"+result
    else:
        result="1"+result


print(int(result,2))

Solution (Python):
def g(x):
    ret = 1 if x % 4 in {1, 2} else 0
    for i in range(1, 50):
        if x % (2 << i) >= (1 << i) and not x % 2:
            ret += (1 << i)
    return ret


A, B = map(int, input().split())
print(g(A - 1) ^ g(B))

Solution (Python):
A,B=map(int,input().split())
ans=0
if A%2==0:
    if B%2==0:
        a=B-A
        a=a//2
        a=a%2
        if a==1:
            print(B+1)
        else:
            print(B)
    else:
        a=B-A+1
        a=a//2
        if a%2==0:
            print(0)
        else:
            print(1)
else:
    if B%2==1:
        a=B-A
        a=a//2
        if a%2==0:
            print(A)
        else:
            print(A-1)
    else:
        a=B-A-1
        a=a//2
        if a%2==1:
            A=A-1
        for i in range(60):
            a1=A%2
            b1=B%2
            ans+=((a1+b1)%2)*2**(i)
            A=A//2
            B=B//2
        print(ans)

Solution (Python):
a, b = map(int, input().split())
x = 0
if  a == b:
    print(a)
else:
    if a % 2 == 1:
        x ^= a
        a += 1
    if b % 2 == 0:
        x ^= b
        b -= 1
    num = b - a + 1
    num //= 2
    if num %2 == 1:
        x ^= 1
    print(x)

Solution (Python):
from collections import deque
from heapq import heapify,heappop,heappush,heappushpop
from copy import copy,deepcopy
from itertools import product,permutations,combinations,combinations_with_replacement
from collections import defaultdict,Counter
from bisect import bisect_left,bisect_right


from functools import reduce
from pprint import pprint

INF = float("inf")

def mycol(data,col):
    return [ row[col] for row in data ]

def mysort(data,col,reverse_flag):
    data.sort(key=lambda x:x[col],reverse=reverse_flag)
    return data

def mymax(data):
    M = -1*float("inf")
    for i in range(len(data)):
        m = max(data[i])
        M = max(M,m)
    return M

def mymin(data):
    m = float("inf")
    for i in range(len(data)):
        M = min(data[i])
        m = min(m,M)
    return m

def mycount(ls,x):
    
    l = bisect_left(ls,x)
    r = bisect_right(ls,x)
    return (r-l)

def myoutput(ls,space=True):
    if space:
        if len(ls)==0:
            print(" ")
        elif type(ls[0])==str:
            print(" ".join(ls))
        elif type(ls[0])==int:
            print(" ".join(map(str,ls)))
        else:
            print("Output Error")
    else:
        if len(ls)==0:
            print("")
        elif type(ls[0])==str:
            print("".join(ls))
        elif type(ls[0])==int:
            print("".join(map(str,ls)))
        else:
            print("Output Error")

def I():
    return int(input())

def MI():
    return map(int,input().split())

def RI():
    return list(map(int,input().split()))

def CI(n):
    return [ int(input()) for _ in range(n) ]

def LI(n):
    return [ list(map(int,input().split())) for _ in range(n) ]

def S():
    return input()

def MS():
    return input().split()

def RS():
    return list(input().split())

def CS(n):
    return [ input() for _ in range(n) ]

def LS(n):
    return [ list(input().split()) for _ in range(n) ]

a,b = MI()






b += 1

k = 43
ls = [0]*k
for i in range(k):
    t = 2**(i+1)
    cb = (t//2)*(b//t) + max( 0, (b%t)-(t//2) )
    ca = (t//2)*(a//t) + max( 0, (a%t)-(t//2) )
    c = cb - ca
    
    if c%2==0:
        ls[i] = 0
    else:
        ls[i] = 1    


ans = 0
for i in range(k):
    ans += ls[i]*(2**i)
print(ans)

Solution (Python):
def F(A, B):
    tmp = A
    for i in range(A, B):
        tmp = tmp^(i+1)
    return tmp

def f(A):
    tmp = A%4
    if tmp == 0:
        ans = 0^A
    elif tmp == 1:
        ans = 1
    elif tmp == 2:
        ans = 1^A
    else:
        ans = 0
    return ans

def main():
    A, B = map(int, input().split())
    
    ans = f(B)^f(A-1)
    print(ans)

if __name__ == "__main__":
    main()

Solution (Python):
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()

from collections import defaultdict, deque, Counter
from sys import exit
import heapq
import math
import copy
from operator import mul
from functools import reduce
from bisect import bisect_left, bisect_right

import sys
sys.setrecursionlimit(1000000000)
mod = 10 ** 9 + 7

A, B = getNM()





flags1 = [0] * 61
flags2 = [0] * 61

def bitflag(n, flaglist):
    if n > 0:
        for i in range(1, 61):
            split = 2 ** i
            flag1 = (n // split) * (split // 2)
            flag2 = max(n % split + 1 - (split // 2), 0)
            flaglist[i] += flag1 + flag2

bitflag(A - 1, flags1)
bitflag(B, flags2)
for i in range(61):
    flags2[i] -= flags1[i]
ans = 0

for i in range(61):
    if flags2[i] % 2 != 0:
        ans += 2 ** (i - 1)
print(ans)

Solution (Python):



A,B = map(int, input().split())


if A == B:
    print(B)
    exit()
elif B - A == 1:
    print(A ^ B)
    exit()

"""
1 xor 1 = 0
0 xor AAA = AAA
(2*n) xor ((2*n)+1) = 1

とか。

"""
if A % 2 == 0:
    if B % 2 == 1:
        cnt_1 = (B - A + 1) // 2
        if cnt_1 % 2 == 0:
            ans = 0
        else:
            ans = 1
    else:
        cnt_1 = (B-1 - A + 1) // 2
        if cnt_1 % 2 == 0:
            ans = B
        else:
            ans = 1 ^ B
else:
    if B % 2 == 1:
        cnt_1 = (B - (A+1) + 1) // 2
        if cnt_1 % 2 == 0:
            ans = A
        else:
            ans = 1 ^ A
    else:
        cnt_1 = (B-1 - (A+1) + 1) // 2
        if cnt_1 % 2 == 0:
            ans = A ^ B
        else:
            ans = A ^ 1 ^ B
print(ans)

Solution (Python):

import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import Counter, deque
from collections import defaultdict
from itertools import combinations, permutations, accumulate, groupby, product
from bisect import bisect_left,bisect_right
from heapq import heapify, heappop, heappush
from math import floor, ceil,pi
from operator import itemgetter
def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))
def LI2(): return [int(input()) for i in range(n)]
def MXI(): return [[LI()]for i in range(n)]
def SI(): return input().rstrip()
def printns(x): print('\n'.join(x))
def printni(x): print('\n'.join(list(map(str,x))))
inf = 10**17
mod = 10**9 + 7

a,b=MI()
def accumbi(x):
    ans=((x+1)//2)%2
    i=1
    while 2**(i-1)<x:
        ans+=(2**i)*((max(0,x%(2**(i+1))-2**i+1))%2)
        i+=1
    return ans
print(accumbi(b)^accumbi(a-1))

Solution (Python):


import sys






















def main():
    mod = 1000000007                
    inf = float('inf')              
    
    sys.setrecursionlimit(10**6)    
    def input(): return sys.stdin.readline().rstrip()
    def ii():    return int(input())
    def mi():    return map(int, input().split())
    def mi_0():  return map(lambda x: int(x)-1, input().split())
    def lmi():   return list(map(int, input().split()))
    def lmi_0(): return list(map(lambda x: int(x)-1, input().split()))
    def li():    return list(input())
    
    
    def calc_xor(num, digit):
        '0 to num について、下の桁から順に xor を取った時の結果を buf に append して返す'
        buf = [0] * digit
        for i in range(len(bin(num)[2:])):
            if i == 0:
                blocks = (num + 1) // pow(2, i + 1)
                buf[i] = blocks % 2
            else:
                res = (num + 1) % pow(2, i + 1)
                buf[i] = max(res - pow(2, i), 0) % 2
        
        return buf



    a, b = mi()
    digit = len(bin(b)[2:])
    f_a = calc_xor(a-1, digit) if a != 0 else [0] * digit
    f_b = calc_xor(b, digit)
    
    ans = 0
    for i in range(digit):
        ans += pow(2, i) * ((f_b[i] - f_a[i]) % 2)
    print(ans)


if __name__ == "__main__":
    main()

Solution (Python):
import sys
def input(): return sys.stdin.readline().rstrip()

def main():
    a,b=map(int,input().split())
    x=(((b-1)//2)-(a-1)//2)%2
    if a%2==0:
        if b%2==0:print(x^b)
        else:print(x)
    else:
        if b%2==0:print(a^x^b)
        else:print(a^x)

if __name__=='__main__':
    main()

Solution (Python):
import sys
def input(): return sys.stdin.readline().rstrip()

def main():
    a,b=map(int,input().split())
    x=(((b-1)//2)-(a-1)//2)%2
    if a%2==0:
        if b%2==0:print(x^b)
        else:print(x)
    else:
        if b%2==0:print(a^x^b)
        else:print(a^x)

if __name__=='__main__':
    main()

Solution (Python):
A,B = (int(x) for x in input().split())
if A == 0:
    m = B % 4
    if m == 0:
        print(B)
    elif m == 1:
        print('1')
    elif m == 2:
        print(B^1)
    else:
        print('0')
else:
    ma = (A-1) % 4
    mb = B % 4
    if ma == 0:
        xora = A-1
    elif ma == 1:
        xora = 1
    elif ma == 2:
        xora = (A-1) ^ 1
    else:
        xora = 0
    if mb == 0:
        xorb = B
    elif mb == 1:
        xorb = 1
    elif mb == 2:
        xorb = B ^ 1
    else:
        xorb = 0
    print(xora^xorb)

Solution (Python):
a, b = map(int, input().split())


def solve(n):
    m = (n // 4) * 4
    res = m
    for i in range(m + 1, n + 1):
        res ^= i
    return res

print(solve(b) ^ solve(a - 1))

Solution (Python):
a, b = map(int, input().split())

def odd(x):
    if ( (x + 1) // 2 ) % 2 == 0:
        return 0
    else:
        return 1

def solve(m):
    if m % 2 == 1:
        return odd(m)
    else:
        return odd(m + 1) ^ (m + 1)

print(solve(b) ^ solve(a - 1))

Solution (Python):

import sys


def g(n: int):
    
    
    
    
    

    ans = 0
    ans += [0, 1, 1, 0][n % 4]
    for i in range(1, 64):
        k = n % 2 ** (i + 1)
        if k < 2 ** i:
            continue
        if k % 2 == 0:
            ans += 1 << i
    return ans


def solve(A: int, B: int):
    print(g(B) ^ g(A - 1))


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    A = int(next(tokens))  
    B = int(next(tokens))  
    solve(A, B)


if __name__ == '__main__':
    main()

Solution (Python):
import sys
def input(): return sys.stdin.readline().strip()

def f(a):
    """
    (0 ^ 1 ^ 2 ^ ... ^ a)を返す関数。
    各ビットにおける1の個数をカウントしなくても、
            (2k) ^ (2k+1) = 0
    であることを使えばO(1)で求まる。例えば
    0 ^ 1 ^ 2 ^ 3 ^ 4 ^ 5 ^ 6 = (0 ^ 1) ^ (2 ^ 3) ^ (4 ^ 5) ^ 6
                              =    1    ^    1    ^    1    ^ 6
                              =    1    ^    6
    """
    if a % 4 == 3: return 0
    if a % 4 == 1: return 1
    if a % 4 == 2: return 1 ^ a
    if a % 4 == 0: return a


def main():
    A, B = map(int, input().split())
    print(f(A - 1) ^ f(B))


if __name__ == "__main__":
    main()

Solution (Python):
import sys
def input(): return sys.stdin.readline().strip()

def f(a, n): 
    if a == 0: return 0
    if n == 0 and (a % 4 == 0 or a % 4 == 3): return 0
    if n == 0 and (a % 4 == 1 or a % 4 == 2): return 1
    idx = a // (2 ** n)
    if idx % 2 == 0: return 0
    return (a - idx * 2**n + 1) % 2

def g(a, b, n): 
    if a == 0: return f(b, n)
    return (f(b, n) + f(a-1, n)) % 2


def main():
    A, B = map(int, input().split())
    ans = 0
    for i in range(41):
        ans += g(A, B, i) * 2**i
        
    print(ans)


if __name__ == "__main__":
    main()

Solution (Python):
def xor(n):
    num_pair = (n - 1) // 2
    if num_pair % 2 == 0:
        counter = 1
    else:
        counter = 0

    if n % 2 == 0:
        return n ^ counter
    else:
        return counter


a, b = map(int, input().split())

print(xor(b) ^ xor(a - 1))

Solution (Python):
A,B = map(int,input().split())
def f(B):
  return ((B+1)%2==0)*((B+1)//2%2==1) + ((B+1)%2!=0)*(((B+1)//2%2==1)^B)
print(f(A-1)^f(B))

Solution (Python):
A,B = map(int, input().split())

fa = 0
if A%2 == 0 and A%4 == 0:
    fa = 0
elif A%2 == 0 and A%4 != 0:
    fa = 1
elif A%2 != 0 and (A-1)%4 == 0:
    fa = ((A-1) ^ 0)
elif A%2 != 0 and (A-1)%4 != 0:
    fa = (A-1) ^ 1

fb = 0
if (B+1)%2 == 0 and (B+1)%4 == 0:
    fb = 0
elif (B+1)%2 == 0 and (B+1)%4 != 0:
    fb = 1
elif (B+1)%2 != 0 and B%4 == 0:
    fb = (B ^ 0)
elif (B+1)%2 != 0 and B%4 != 0:
    fb = (B ^ 1)

print(fa ^ fb)

Solution (Python):
a, b = map(int, input().split())
def f(x):
    if x%2: return-(-x//2)%2
    else: return (x//2)%2+x
print(f(a-1)^f(b))

Solution (Python):
a,b=map(int,input().split())
def func(n,m):
  c=m//pow(2,n)
  d=m%pow(2,n)
  
  if c%2==0:
    return pow(2,n)*(c//2)
  else:
    return pow(2,n)*((c-1)//2)+d+1
i=0
while pow(2,i)<=b:
  i+=1
maxn=i
ans=0
for i in range(maxn+1):
  e=func(i,b)-func(i,max(0,a-1))
  if e%2==1:
    ans+=pow(2,i)
print(ans)

Solution (Python):
def f(A, B):
    assert A <= B
    if A % 2 == 0 and B % 2 == 1:
        return ((B - A + 1) // 2) % 2
    if A % 2 == 0 and B % 2 == 0:
        return (((B - A) // 2) % 2) ^ B
    if A % 2 == 1 and B % 2 == 1:
        return A ^ (((B - A) // 2) % 2)
    if A % 2 == 1 and B % 2 == 0:
        return A ^ (((B - A - 1) // 2) % 2) ^ B


def main():
    A, B = list(map(int, input().split(' ')))
    print(f(A, B))


if __name__ == '__main__':
    main()

Solution (Python):
A,B = map(int,(input().split()))
def xor(n):
    if n%2 == 1:
        if (n+1)%4 == 0:
            return 0
        else:
            return 1
    else:
        if n%4 == 0:
            return n^0
        else:
            return n^1
            
print(xor(A-1)^xor(B))

Solution (Python):
import bisect,collections,copy,heapq,itertools,math,numpy,string
import sys
def S(): return sys.stdin.readline().rstrip()
def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int,sys.stdin.readline().rstrip().split())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LS(): return list(sys.stdin.readline().rstrip().split())



a,b = MI()

if a % 2 == 0:
    if b % 2 == 0:
        if (b-a) % 4 == 2:
            print(b + 1)
        else:
            print(b)
    else:
        if (b-a) % 4 == 1:
            print(1)
        else:
            print(0)
else:
    if b % 2 == 0:
        if (b-a) % 4 == 1:
            bst = bin(b)
            ast = bin(a)
            anst = '0b'
            if len(bst) - len(ast) > 0:
                for i in range(len(bst) - len(ast)):

                    anst += bst[2+i]
            for i in range(len(ast) -2):
                if ast[-len(ast) + 2 + i] == bst[-len(ast) + 2 + i]:
                    anst += '0'
                else:
                    anst += '1'
                aa = int(anst[2:],2)
            print(aa)

        else:
            bst = bin(b)
            ast = bin(a)
            anst = '0b'
            if len(bst) - len(ast) > 0:
                for i in range(len(bst) - len(ast)):
                    anst += bst[2 + i]
            for i in range(len(ast) - 2):
                if ast[-len(ast) + 2 + i] == bst[-len(ast) + 2 + i]:
                    anst += '0'
                else:
                    anst += '1'
                aa = int(anst[2:], 2)
            print(aa - 1)
    else:
        if (b-a) % 4 == 2:
            print(a-1)
        else:
            print(a)

Solution (Python):
import sys
readline = sys.stdin.readline

def f(x):
    if x % 2 == 0:
        if (x//2) % 2 == 0:
            return x ^ 0
        else:
            return x ^ 1
    else:
        if ((x+1)//2) % 2 == 0:
            return 0
        else:
            return 1

def main():
    A, B = map(int, readline().rstrip().split())
    print(f(A-1) ^ f(B))

if __name__ == '__main__':
    main()

Solution (Python):
def f(n):
    num=n%4
    if num==0:return n
    elif num==1:return 1
    elif num==2:return n+1
    else:return 0


a,b=map(int,input().split())
print(f(a-1)^f(b))

Solution (Python):
def count1(x, m):
  return x // (2 * m) * m + max(0, x % (2 * m) - m)

a, b = map(int, input().split())
ans = 0
m = 1
while m <= 2 * b:
  ans += (count1(b + 1, m) - count1(a, m)) % 2 * m
  m *= 2
print(ans)

Solution (Python):
A,B=map(int,input().split())
k=A%4
AA=A+4-k
l=B%4
BB=B-l
AAA=[]
BBB=[]
for i in range(A,AA):
    AAA+=[i]
for i in range(BB,B+1):
    BBB+=[i]

def henkan(A):
    if len(A)==4 or len(A)==0:
        return 0
    elif len(A)==3:
        return A[0]^A[1]^A[2]
    elif len(A)==2:
        return A[0]^A[1]
    elif len(A)==1:
        return A[0]
print(henkan(AAA)^henkan(BBB))

Solution (Python):
a,b=map(int,input().split())
print((a*(a%2))^(b*(b%2==0))^(((b-a+(a%2==0 and b%2))//2)%2))

Solution (Python):

import sys


def f(n):
    '''
    >>> f(1)
    1
    >>> f(6)
    7
    '''
    return (0 if n % 2 else n) ^ (1 if (n+1) // 2 % 2 else 0)


def solve(A: int, B: int):
    return f(A-1) ^ f(B)



def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    A = int(next(tokens))  
    B = int(next(tokens))  
    print(solve(A, B))

def test():
    import doctest
    doctest.testmod()

if __name__ == '__main__':
    test()
    main()

Solution (Python):

import sys


def f(B, d):
    '''
    >>> f(6, 0) 
    3
    >>> f(6, 1) 
    3
    >>> f(6, 2) 
    3
    >>> f(6, 3)
    0
    '''
    r = 2**(d+1)
    rr = 2 ** d
    return B // r * rr + max(B % r - rr + 1, 0)
    
def g(A, B, d):
    '''
    >>> g(0, 6, 0) 
    3
    >>> g(0, 6, 1) 
    3
    >>> g(0, 6, 2) 
    3
    >>> g(2, 6, 0) 
    2
    '''
    if A == 0:
        return f(B, d)
    return f(B, d) - f(A-1, d)

def solve(A: int, B: int):
    ans = 0
    for d in range(10000, -1, -1):
        ans <<= 1
        ans += g(A, B, d) % 2
    return ans



def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    A = int(next(tokens))  
    B = int(next(tokens))  
    print(solve(A, B))

def test():
    import doctest
    doctest.testmod()

if __name__ == '__main__':
    test()
    main()

Solution (Python):
a, b = map(int, input().split())
def f(n):
    if n % 2:
        return -(-n//2) % 2
    else:
        return (n//2) % 2 + n
print(f(a - 1) ^ f(b))

Solution (Python):
a, b = [int(x) for x in input().split()]

def f_xor(n):
    temp = (n // 2) % 2
    if n % 2 == 0:
        temp ^= n
    else:
        temp ^= 1
    return temp

if a == 0:
    print(f_xor(b))
else:
    print(f_xor(a - 1) ^ f_xor(b))

Solution (Python):
a, b = map(int, input().split())
def f(n):
    if n % 2:
        return 1 if -(-n//2) % 2 else 0
    else:
        return 1 + n if (n//2) % 2 else n 
print(f(a - 1) ^ f(b))

Solution (Python):
def calc(x):
    if x % 4 == 1:
        return 1
    if x % 4 == 3:
        return 0
    
    if x % 4 == 2:
        return 1 + x
    else:
        return x




A, B = map(int, input().split())
x = calc(A - 1)
y = calc(B)
print(x ^ y)

Solution (Python):
a,b=map(int,input().split())

def calc(x):
    n = x // 2 % 2
    if x % 2 :
        if n : return 0
        else: return 1 
    else:
        return x ^ n 

print(calc(b) ^ calc(a-1))

Solution (Python):
a, b = map(int, input().split())
if a == b:
    print(a)
else:
    if a % 2 == 0 and b % 2 == 1:
        if (b-a+1) % 4 == 0:
            print(0)
        else:
            print(1)
    elif a % 2 == 0 and b % 2 == 0:
        if (b-a) % 4 == 0:
            print(b)
        else:
            print(b^1)
    elif a % 2 == 1 and b % 2 == 1:
        if (b-a) % 4 == 0:
            print(a)
        else:
            print(a^1)
    elif a % 2 == 1 and b % 2 == 0:
        if (b-a-1) % 4 == 0:
            print(a^b)
        else:
            print((a^b)^1)

Solution (Python):
a, b = map(int, input().split())
c, d = a, b
l = []
m = []
n = []
t = 0
while b > 0:
    l.append(b%2)
    b //= 2
k = len(l)
for i in range(k):
    m.append(a%2)
    a //= 2
if d%2 == 1:
    l = [0]*(k)
if c%2 == 0:
    m = [0]*(k)
for i in range(k):
    n.append((l[i]+m[i])%2)
c = (c+1)//2*2
d = (d+1)//2*2
if (d-c)%4 == 2 or (d-c)%4 == 3:
    n[0] = (n[0]+1)%2
for i in range(k):
    t += n[i]*(2**i)
print(t)

Solution (Python):
import numpy as np

A, B = map(int, input().split())


if A % 2 == 0:
    if B % 2 == 0:
        
        if ((B - A) / 2) % 2 == 0:
            print(int(bin(B ^ 0), 2))
        else:
            print(int(bin(B ^ 1), 2))
    else:
        
        if ((B - A + 1) / 2) % 2 == 0:
            print(0)
        else:
            print(1)
else:
    if B % 2 == 0:
        
        if ((B-A-1) / 2) % 2 == 0:
            print(int(bin(B ^ A), 2))
        else:
            print(int(bin(B ^ A ^ 1), 2))
    else:
        
        if ((B-A) / 2) % 2 == 0:
            print(A)
        else:
            print(A ^ 1)

Solution (Python):
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for _ in range(N)]
def dp2(ini, i, j): return [[ini]*i for _ in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for _ in range(j)] for _ in range(k)]




A, B = mi()

ans = 0

def count(n):
    if n==0:
        return 0
    N = n
    n %= 4
    if n == 1:
        return 1
    if n == 2:
        return N+1
    if n == 3:
        return 0
    if n == 0:
        return N

print(count(A-1)^count(B))

Solution (Python):
A, B = map(int, input().split())
bin_A = bin(A - 1)
bin_B = bin(B)
A_xor = [0 for _ in range(len(bin_B) - 2)]
B_xor = [0 for _ in range(len(bin_B) - 2)]
for i in range(len(bin_B)):
    if i == 0:
        if B % 4 == 1 or B % 4 == 2:
            B_xor[i] = 1
    else:  
        if (B // pow(2, i)) % 2 == 1 and (B % pow(2, i)) % 2 == 0:
            B_xor[i] = 1
if A == 0:
    print(int("".join(map(str, B_xor[::-1])), 2))
    exit()
for i in range(len(bin_A)):
    if i == 0:
        if (A - 1) % 4 == 1 or (A - 1) % 4 == 2:
            A_xor[i] = 1
    else:
        if ((A - 1) // pow(2, i)) % 2 == 1 and ((A - 1) % pow(2, i)) % 2 == 0:
            A_xor[i] = 1
ans = []
for a, b in zip(A_xor, B_xor):
    if a != b:
        ans.append(1)
    else:
        ans.append(0)
print(int("".join(map(str, ans[::-1])), 2))

Solution (Python):
n, m = map(int, input().split())

def cumXOR(k):
    if k % 4 == 0:
        return k
    elif k % 4 == 1:
        return 1
    elif k % 4 == 2:
        return k + 1
    else:
        return 0

print(cumXOR(n-1)^cumXOR(m))

Solution (Python):
A,B=map(int,input().split());B+=1
print(sum(((((B//(2*(2**j)))*(2**j)+max(0,(B%(2*(2**j)))-2**j))-((A//(2*(2**j)))*(2**j)+max(0,(A%(2*(2**j)))-2**j)))%2)*(2**j) for j in range(41)))