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):
import sys
sys.setrecursionlimit(4100000)

import math

import logging

logging.basicConfig(level=logging.DEBUG)

logger = logging.getLogger(__name__)

















def resolve():
    
    
    A, B = [int(x) for x in sys.stdin.readline().split()]  
    

    
    
    
    

    logger.debug('{}'.format([]))

    if A == 0 and B == 0:
        print(0)
        return

    if A == 0:
        A = 1

    k = 0
    digit = 1 / 2
    result_bin = []
    while (digit < B):
        k += 1
        digit = int(2 * digit)
        offset = digit - 1
        period = 2 * digit
        
        if (A - offset) <= 0 and (B - offset) <= 0:
            result_bin.append(0)
            continue
        
        if (A - offset) <= 0 and (B - offset) > 0:
            mb = get_m(B, period, offset)
            result_bin.append(under_b(mb, digit))
            continue

        ma = get_m(A, period, offset)
        mb = get_m(B, period, offset)
        
        
        if math.ceil((A - offset) / period) == math.ceil(
            (B - offset) / period):

            if ma < digit and mb < digit:
                result_bin.append(mb - ma + 1)
                continue
            elif ma < digit and digit <= mb:
                result_bin.append(digit - ma)
                continue
            else:
                result_bin.append(0)
                continue

        
        if k == 1:
            result_bin.append(
                upper_a(ma, digit) + under_b(mb, digit) +
                math.ceil((B - offset) / period) -
                math.ceil((A - offset) / period) - 1)
            continue
        result_bin.append(upper_a(ma, digit) + under_b(mb, digit))
        continue

    print(int(''.join([str(x % 2) for x in reversed(result_bin)]), 2))


def get_m(x, period, offset):
    return ((x - offset - 1) % period)


def upper_a(m, digit):
    if m >= digit:
        return 0
    else:
        return digit - m


def under_b(m, digit):
    if m >= digit:
        return digit
    else:
        return m + 1


if __name__ == "__main__":
    resolve()





import sys
from io import StringIO
import unittest


class TestClass(unittest.TestCase):
    def assertIO(self, input, output):
        stdout, stdin = sys.stdout, sys.stdin
        sys.stdout, sys.stdin = StringIO(), StringIO(input)
        resolve()
        sys.stdout.seek(0)
        out = sys.stdout.read()[:-1]
        sys.stdout, sys.stdin = stdout, stdin
        self.assertEqual(out, output)

    def test_入力例_1(self):
        input = """2 4"""
        output = """5"""
        self.assertIO(input, output)

    def test_入力例_2(self):
        input = """123 456"""
        output = """435"""
        self.assertIO(input, output)

    def test_入力例_3(self):
        input = """123456789012 123456789012"""
        output = """123456789012"""
        self.assertIO(input, output)

Solution (Python):
a, b = map(int, input().split())
 
def g(x):
  y = x % 4
  if y == 0: return x
  if y == 1: return 1
  if y == 2: return x ^ 1
  if y == 3: return 0
  
print(g(a-1) ^ g(b))

Solution (Python):
from sys import stdin
a,b = map(int,stdin.readline().rstrip().split())

def xor(n):
    point = ((n+1)//2)%2
    if n%2 == 0:
        if point == 0:
            return 0^n
        else:
            return 1^n
    else:
        if point == 0:
            return 0
        else:
            return 1
print(xor(a-1)^xor(b))

Solution (Python):

def F(A):
    if A%2==0:
        if (A//2)%2==0:
            return A
        else:
            return 1^A
    else:
        if ((A+1)//2)%2==0:
            return 0
        else:
            return 1
def f(A,B):
    return F(A-1)^F(B)

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

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

A_bit = [0] * 40
B_bit = [0] * 40

A -= 1
i = 0
while True:
  a_shou, a_amari = divmod(A, 2**i)
  if 2**i > A+1 :
    break
  if a_shou % 2 == 0:
    A_bit[i] = (a_shou//2) * (2**i)
  else:
    A_bit[i] = (a_shou//2) * (2**i) + a_amari + 1
  i += 1

j = 0
while True:
  b_shou, b_amari = divmod(B, 2**j)
  if 2**j > B+1 :
    break
  if b_shou % 2 == 0:
    B_bit[j] = (b_shou//2) * (2**j)
  else:
    B_bit[j] = (b_shou//2) * (2**j) + b_amari + 1
  j += 1
ans = 0
for i in range(40):
  if (B_bit[i] - A_bit[i]) % 2 == 0:
    continue
  else:
    ans += 2**i
    
print(ans)

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

def f(x):
    d = {}
    for i in range(45):
        k = 2**i
        if x-k<0:
            d[i] = 0
        else:
            A = (x-k)//k
            v = k*(A-A//2)
            if A%2==0:
                v += x-(A+1)*k+1
            d[i] = v
    return d

b = f(B)
for i,j in f(A-1).items():
    b[i] -= j

ans = 0
for i,j in b.items():
    if j%2:
        ans += 2**i
print(ans)

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

def calc(n):
    lst = []
    if n==-1:return '0b0'
    if n%4==1 or n%4==2:lst.append('1')
    else:lst.append('0')
      
    mm = 2
    
    while n//mm != 0:
        l = n%(2*mm)
        if l >= mm and l%2==0:
            lst.append('1')
        else:lst.append('0')
        mm *= 2
    lst.append('0b')
    lst.reverse()
    return ''.join(lst)

lsta = int(calc(a-1),0)
lstb = int(calc(b),0)

print(lsta^lstb)

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

if a % 2 == 0:
    r = (b - (a + 3)) % 4
    answer = 0
else:
    r = (b - a) % 4
    answer = a
for i in range(r):
    answer ^= b - i

print(answer)

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

def search_cycle(k):
    return 1 << (k+1)

def func(x): 
    if x == 0:
        return 0
    ans = 0
    for i in range(40):
        loop = search_cycle(i)
        count = (x//loop)*(loop//2)
        amari = max(0,x%loop-loop//2)
        count += amari

        if count %2 != 0:
            ans += 1 << i
    return ans

print(func(b+1)^func(a))

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

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

Solution (Python):
def baseorder(num):
    i=0
    while num>=2**(i+1):
        i+=1
    return i

def function(num):
    if num==0:
        return 0
    elif num==1:
        return 1
    elif num==2:
        return 3
    elif num==3:
        return 0
    else:
        x=baseorder(num)
        return (2**x)*((num-2**x+1)%2)+function(num-2**x)

A,B=map(int,input().split())
if A==0:
    print(function(B))
else:
    print(function(B)^function(A-1))

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


def f(A, B):
    if A == 0:

        if B % 2 == 0:
            return B ^ (B // 2) % 2
        else:
            return 1 ^ (B // 2) % 2

    else:
        return f(0, B) ^ f(0, A - 1)


print(f(A, B))

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

def func2(m):
    n=m+1
    if n%4==0:
        return 0
    if n%2==0:
        return 1
    elif (n+1)%4 ==0:
        return n
    else:
        return n-1

def func(a,b):
    return func2(a-1) ^ func2(b)

print(func(a,b))

Solution (Python):
def main():
  a,b=map(int,input().split())
  
  import math
  def xorsum(n):
    if n%4==0:
      return n
    elif n%4==1:
      return 1
    elif n%4==2:
      return n+1
    else:
      return 0

  print(xorsum(b)^xorsum(a-1))
if __name__=='__main__':
  main()

Solution (Python):
A, B = map(int, input().split())
ra, rb = A%4, B%4

ans = 0
if B - A < 4:
  for i in range(A, B+1):
    ans ^= i
else:
  if ra:
    for i in range(4-ra):
      ans ^= A + i

  for i in range(rb+1):
    ans ^= B - i

print(ans)

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

Solution (Python):
a,b=map(int,input().split())
counter=0
for i in range(40):
    K=2**(i+1)
    judge=0
    u,x=divmod(a,K)
    v,y=divmod(b,K)
    if u==v:
        if y<2**i:
            pass
        elif y>=2**i:
            if x<2**i:
                judge+=(y-2**i+1)
                
            elif x>=2**i:
                judge+=(y-x+1)
    elif u<v:
        judge+=(2**(i+1)-2**i)*(v-u-1)
        if y<2**i:
            pass
        if y>=2**i:
            judge+=y-2**i+1
            
        if x<2**i:
            judge+=2**(i+1)-2**i
        if x>=2**i:
            judge+=2**(i+1)-x
    if judge%2!=0:
        counter+=2**i


print(counter)

Solution (Python):
def acc_xor(n):
    if n % 4 == 0:
        return 0 ^ n
    elif n % 4 == 1:
        return 1
    elif n % 4 == 2:
        return 1 ^ n
    elif n % 4 == 3:
        return 0


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

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


main()

Solution (Python):
def calculate(m,n):
    s1 = calculate2(m-1)
    s2 = calculate2(n)
    return xor(s1,s2)


def calculate2(n):
    if n % 2 == 1:
        if ((n - 1) / 2) % 2 == 0:
            return xor(xor(0,n-1),n)
        else:
            return xor(xor(1,n-1),n)

    else:
        if ((n / 2) % 2) == 0:
            return xor(0,n)
        else:
            return xor(1,n)

def xor(m,n):
    return n ^ m


S = input().split(" ")

result = calculate(int(S[0]),int(S[1]))

print(result)

Solution (Python):
def xor(x):
    if x % 2 == 1:
        return (x // 2 + 1) % 2
    else:
        return xor(x - 1) + x


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

Solution (Python):
x = list(map(int, input().split()))
a = [x[0]-1, x[1]]
ans = 0
for i in a:
    n = i%4
    if n == 1:
        as1 = 1
    elif n == 2:
        as1 = 1^i
    elif n == 3:
        as1 = 0
    else:
        as1 = 0^i
    ans = ans^as1

print(ans)

Solution (Python):

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

def calc(x):
  if x <= 0:
    return 0
    
  ans = 0

  
  for i in range(50):
      
      
      
      
      loop = 2 ** (i+1)
      cnt = (x // loop) * (loop // 2)
      cnt += max(0, (x % loop) - (loop // 2) + 1)

      
      if cnt % 2 == 1:
          ans += 1 << i
 
  return ans

ans = calc(B) ^ calc(A-1)
 
print(ans)

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

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




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

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

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

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

    ans = 0
    for i in (A - 1, B):
        if i % 4 == 0:
            ans ^= i
        elif i % 2 == 0:
            ans ^= i ^ 1
        elif (i + 1) % 4 != 0:
            ans ^= 1
    print(ans)

if __name__ == '__main__':
    main()

Solution (Python):
A, B = map(int, input().split())
a = A % 2
b = B % 2

diff = B - A + 1

if a == 0 and b == 0:
    diff -= 1
    ans = 1 ^ B if diff % 4 == 2 else B    
elif a == 0 and b == 1:
    ans = 1 if diff % 4 == 2 else 0
elif a == 1 and b == 0:
    diff -= 2
    ans = A ^ 1 ^ B if diff % 4 == 2 else A ^ B
else:
    diff -= 1
    ans = A ^ 1 if diff % 4 == 2 else A
print(ans)

Solution (Python):
A, B = map(int, input().split())
ans_list = []
ans = ""
b_cnt = len(bin(B)[2:])

a_list = [0] * b_cnt
b_list = [0] * b_cnt
diff = B - A + 1
for i in range(b_cnt):
    a_tmp = A % (2 ** (i + 1))
    b_tmp = B % (2 ** (i + 1))
    a_list[i] = a_tmp
    b_list[i] = b_tmp

for i in range(b_cnt):
    a = a_list[i]
    b = b_list[i]
    cnt = 0
    if i == 0:
        if a == b == 1:
            cnt += diff//2 + 1
        else:
            cnt += diff//2
    else:
        
        if 2 ** i > a:
            cnt += 0
        else:
            cnt += 2 ** (i+1) - a
        
        if 2 ** i > b:
            cnt += 0
        else:
            cnt += b - 2 ** i + 1
    if cnt % 2 == 0:
        ans_list.append("0")
    else:
        ans_list.append("1")

for i in range(len(ans_list) - 1, -1, -1):
    ans += ans_list[i]

print(int(ans, 2))

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

Solution (Python):
def F(N):
    if N%2 == 0:
        if N%4 == 0:
            return 0^N
        else:
            return 1^N
    else:
        if (N+1)%4 == 0:
            return 0
        else:
            return 1

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

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

Solution (Python):
def f(n):
    s = (n + 1) // 2
    if s & 1 == 1:
        if (n + 1)& 1 == 1:
            return 1 ^ n
        else:
            return 1
    else:
        if (n + 1) & 1 == 1:
            return 0 ^ n
        else:
            return 0

def main():
    a, b = map(int, input().split())
    if a == 0:
        print(f(b))
    elif a == b:
        print(a)
    else:
        print(f(a - 1) ^ f(b))

if __name__ == '__main__':
    main()

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

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

Solution (Python):

import re
import math
from copy import deepcopy
import fractions
import random
from heapq import heappop,heappush
import time
import sys
readline = sys.stdin.readline

mod=int(10**9+7)
inf=int(10**20)
class union_find():
    def __init__(self,n):
        self.n=n
        self.P=[a for a in range(N)]
        self.rank=[0]*n
 
    def find(self,x):
        if(x!=self.P[x]):self.P[x]=self.find(self.P[x])
        return self.P[x]
 
    def same(self,x,y):
        return self.find(x)==self.find(y)
 
    def link(self,x,y):
        if self.rank[x]<self.rank[y]:
            self.P[x]=y
        elif self.rank[y]<self.rank[x]:
            self.P[y]=x
        else:
            self.P[x]=y
            self.rank[y]+=1
 
    def unite(self,x,y):
        self.link(self.find(x),self.find(y))
 
    def size(self):
        S=set()
        for a in range(self.n):
            S.add(self.find(a))
        return len(S)

def bin_(num,size):
    A=[0]*size
    for a in range(size):
        if (num>>(size-a-1))&1==1:
            A[a]=1
        else:
            A[a]=0
    return A
def fac_list(n,mod_=0):
    A=[1]*(n+1)
    for a in range(2,len(A)):
        A[a]=A[a-1]*a
        if(mod>0):A[a]%=mod_
    return A
def comb(n,r):return math.factorial(n)//math.factorial(n-r)//math.factorial(r)
def next_comb(num,size):
    x=num&(-num)
    y=num+x
    z=num&(~y)
    z//=x
    z=z>>1
    num=(y|z)
    if(num>=(1<<size)):return False
    else:
        return num
 

 

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


print(l^r)

Solution (Python):
def xor_sum(n):
    ret = 0
    if n%4 == 0:
        return n
    if n%4 == 1:
        return 1
    if n%4 == 2:
        return n+1
    if n%4 == 3:
        return 0

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

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

Solution (Python):
A, B=map(int, input().split())
def f(x, y):
  return ((y-x+1)//2)%2

if A%2==0 and B%2==1:
  print(f(A, B))
elif A%2==1 and B%2==1:
  print(f(A+1, B)^A)
elif A%2==0 and B%2==0:
  print(f(A, B-1)^B)
else:
  print((f(A+1, B-1)^A)^B)

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


def g(x):
    l = x
    while l % 4 != 0:
        l -= 1
    ret = 0
    for i in range(l, x + 1):
        ret ^= i
    return ret


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

Solution (Python):
def f(n):
	out = 0
	i = 1
	while 2**i <= n*4:
		if i == 1:
			mod = n % 4
			if mod in [1,2]:
				out += 1
		else:
			mod = n % (2**i)
			if ((2**i) // 2 <= mod) and (mod % 2 == 0):
				out += (2**(i-1))
		i += 1

	return out

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

untilB = f(B)
untilA_1 = f(A-1)

print(untilB ^ untilA_1)

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

X = A - 1
fX_bit = []
base = 2
for i in range(40):
    if i == 0:
        fX_bit.append(((X + 1) // 2) % 2)
    else:
        if X % base < (base // 2):
            fX_bit.append(0)
        else:
            fX_bit.append((X % base - (base // 2) + 1) % 2)
    
    base <<= 1

fB_bit = []
base = 2
for i in range(40):
    if i == 0:
        fB_bit.append(((B + 1) // 2) % 2)
    else:
        if B % base < (base // 2):
            fB_bit.append(0)
        else:
            fB_bit.append((B % base - (base // 2) + 1) % 2)
    
    base <<= 1

ans = 0
for fXi, fBi in zip(fX_bit[::-1], fB_bit[::-1]):
    ans <<= 1
    ans += (fXi ^ fBi)

print(ans)

Solution (Python):
A,B=map(int,input().split())
N=len(str(bin(B)))-2
    

def calc(b):
    cnt=b//2
    if b%2==0:
        ans=cnt%2
        ans=ans^b
    else:
        ans=(cnt+1)%2
    return ans

print(calc(B) ^ calc(max(0,A-1)))

Solution (Python):
A,B=map(int,input().split())
N=len(str(bin(B)))-2

p=[1]*(N+1)
for i in range(N):
    p[i+1]=p[i]*2
    
def calc(b):
    ans=0
    for i in range(N):
        cnt=(b//p[i+1])*p[i] + max(0,b%p[i+1]-(p[i]-1))
        ans+=cnt%2*p[i]
    return ans

print(calc(B) ^ calc(max(0,A-1)))

Solution (Python):
a,b=map(int,input().split())
def f(n):
  
  m=n//2
  if n % 4 == 0:
    return n
  elif n % 4 == 1:
    return (n-1)^n
  elif n % 4 == 2:
    return (n-2)^(n-1)^n
  else:
    return (n-3)^(n-2)^(n-1)^n
print(f(a-1)^f(b))

Solution (Python):
A,B = map(int,input().split())
def F(X):
    if X%4 ==0:return X
    elif X%4 == 1:
        return 1
    elif X%4 == 2:
        return 1^X
    else:
        return 0
ans = F(B)^F(A-1)
print(ans)

Solution (Python):
a, b = map(int, input().split())
A = format(a, "045b")
B = format(b, "045b")
s = ""
A1 = [(a-1) // (2 ** (i+1)) * 2 ** i + max((a-1) % 2**(i+1) - 2 ** i + 1, 0) for i in range(44, -1, -1)]
B1 = [b // (2 ** (i+1)) * 2 ** i  + max(b % 2 ** (i+1) - 2 ** i + 1, 0) for i in range(44, -1, -1)]  
for i in range(45):
  s += str(int(A1[i]%2 != B1[i]%2))

print(int(s, 2))

Solution (Python):
import math
import sys
a,b=map(int,input().split())
if b==0:
    print(0)
    sys.exit()
n=math.floor(math.log2(b))+1
ans=[0]*n
form="0"+str(n)+"b"
sa=format(a,form)
sb=format(b,form)
for i in range(n):
    if i==n-1:
        if (b-a+1)%2==0:
            ans[i]=((b-a+1)//2)%2
        else:
            if sa[i]=="1":
                ans[i]=((b-a+1)//2+1)%2
            else:
                ans[i]=((b-a+1)//2)%2
        break
    if sa[i]=="1" and sb[i]=="0":
        s_compa=sa[:i]+"1"*(n-i)
        cmpa=int(s_compa,2)
        ans[i]=(cmpa-a+1)%2
    elif sa[i]=="0" and sb[i]=="1":
        s_compb=sb[:i]+"1"+"0"*(n-i)
        cmpb=int(s_compb,2)
        ans[i]=(b-cmpb+1)%2
    elif sa[i]=="1" and sb[i]=="1":
        s_compa=sa[:i]+"1"*(n-i)
        cmpa=int(s_compa,2)
        s_compb=sb[:i]+"1"+"0"*(n-i)
        cmpb=int(s_compb,2)
        if cmpa>a:
            ans[i]=((b-cmpb+1)+(cmpa-a+1))%2
        else:
            ans[i]=(b-a+1)%2
cnt=0
for i in range(n):
    cnt+=(ans[i]*2**(n-i-1))
print(cnt)

Solution (Python):
def calc(A):
    
    ans = 0
    for i in range(50):
        
        
        
        
        loop = 1 << (i+1)
        cnt = (A // loop) * (loop // 2)
        cnt += max(0, (A % loop) - (loop // 2) + 1)

        
        if cnt % 2 == 1:
            ans += 1 << i

    return ans


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

ans = calc(B) ^ calc(A-1)

print(ans)

Solution (Python):
def calc(A):
    if A <= 0:
        return 0

    
    ans = 0
    for i in range(50):
        
        
        
        
        loop = 1 << (i+1)
        cnt = (A // loop) * (loop // 2)
        cnt += max(0, (A % loop) - (loop // 2) + 1)

        
        if cnt % 2 == 1:
            ans += 1 << i

    return ans


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

ans = calc(B) ^ calc(A-1)

print(ans)

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

if a > b: 
    a,b = b,a

"""
制約10**12は、2**40に収まるので、外側のループを2**40にする
>>> 10**12 < 2**40
True

また、aからbまでを愚直に足していくわけには行かず、ここに法則を見出す必要がある。
a,bに対して、
ans = 0~bまでのXOR ^ 0~(a-1)までのXOR (^は演算子でXOR)

ということができる。
あとは、各桁ごとの0~Xに対するXORを求める関数を作れば良い。

法則：
0~Xまでの各桁の2進数表記には周期がある。
2**0桁：0 1 0 1 0 1 0 1 (周期2)
2**1桁：0 0 1 1 0 0 1 1 (周期4)
2**2桁：0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 (周期8)
2**3桁：0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 (周期16)...
2**k桁目の周期 loop = 2*(i+k)
よって、この周期性を式に起こした上で、その桁における1の出現回数の偶奇が0~Xのその桁におけるXORの和
"""

def search_cycle(k): 
    loop = 1<<(k+1) 
    return loop

def func(x): 
    if x==0: return 0
    ans = 0
    for i in range(40): 
        loop = search_cycle(i)
        count = (x//loop) * (loop//2) 
        amari = max(0,x%loop - (loop//2)) 
        
        count += amari
    
        
        if count %2 == 1:
            ans += 1<<i
    
    return ans

print(func(b+1) ^ func(a))

Solution (Python):
A,B = map(int,input().split())
def F(X): 
    if X%4 ==0:return X
    elif X%4 == 1:
        return 1
    elif X%4 == 2:
        return 1^X
    else:
        return 0
ans = F(B)^F(A-1)
print(ans)

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

data=[0 for i in range(40)]
if 10>B-A>=1:
    lst=[i for i in range(A,B+1)]
else:
    lst=[]
    if A%2==1:
        lst.append(A)
        A+=1
    for i in range((B-A+1)%4):
        lst.append(B-i)

    
for num in lst:
    for i,s in enumerate(list(reversed(bin(num)[2:]))):
        data[i]=(data[i]+int(s))%2

while data:
    if data[-1]==0:
        data.pop()
    else:
        break

value=0
for i in range(len(data)):
    if data[i]:
        value+=2**(i)
if data:
    print(value)
else:
    print(0)

Solution (Python):
def f(X):
    res = 0
    
    if X%4 in [1, 2]:
        res += 1
    
    p = 4
    
    for i in range(50):
        if X%p>=p//2 and (X%p-p//2+1)%2==1:
            res += 2**(i+1)
        
        p *= 2
        
    return res

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

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

Solution (Python):
def solve(n):
    """ f(0, n) """

    n += 1
    res = 0
    for i in range(0, 40):
        t2 = (1 << i)
        
        x = n // (t2 * 2)
        cnt = x * t2
        
        cnt += max(0, n % (t2 * 2) - t2)

        res += t2 * (cnt % 2)
    return res


a, b = [int(_) for _ in input().split()]


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

Solution (Python):

import math
import heapq
import bisect
import numpy as np


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

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

print(ans)

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


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


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

Solution (Python):
from math import log2


def cntOnes(n, N):
    ret = [0] * N
    i = 0
    while (n >> i) > 0:
        t = 2 ** i
        quot = n // t
        rem = n % t
        if quot % 2 == 1:
            ret[i] = (quot // 2) * t + (rem + 1)
        else:
            ret[i] = (quot // 2) * t
        i += 1
    return ret


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

if B == 0:
    print(0)
    exit()
dig = int(log2(B)) + 1
cntA = cntOnes(A - 1, dig) if A != 0 else [0] * dig
cntB = cntOnes(B, dig)

ans = 0
for i, (a, b) in enumerate(zip(cntA, cntB)):
    if (a - b) % 2 == 1:
        ans += (1 << i)

print(ans)

Solution (Python):
import sys

def sum_bincount(n):
    l = 0
    r = n
    res = [0] * (41)
    if n < 0:
        return res
    for i in range(40, -1, -1):
        stand = n >> i & 1
        res[i] += 2 ** i * l
        if stand:
            r -= 2 ** i
            res[i] += r + 1
        l = (l << 1) + (stand & 1)
    return res

a, b = map(int, sys.stdin.readline().split())

def main():
    s_a_bin = sum_bincount(a-1)
    s_b_bin = sum_bincount(b)
    res = 0
    for i in range(40, -1, -1):
        res += 2 ** i * ((s_a_bin[i] % 2) ^ (s_b_bin[i] % 2))
    return res

if __name__ == '__main__':
    ans = main()
    print(ans)

Solution (Python):
import sys

def cumxor(n):
    q, r = divmod(n+1, 2)
    return q & 1 ^ (n * r)

a, b = map(int, sys.stdin.readline().split())

def main():
    return cumxor(b) ^ cumxor(a-1)

if __name__ == '__main__':
    ans = main()
    print(ans)

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

def f(a):
    ret=0
    a+=1
    for i in range(40):
        cycle=2<<i
        one_count=(a//cycle)*cycle//2 + max(0, a%cycle - cycle//2)
        if one_count&1:
            ret|=1<<i
        
    return ret

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

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

def f(a):
    e=a%4
    if e==0:
        return a
    elif e==1:
        return (a-1)^a
    elif e==2:
        return (a-2)^(a-1)^a
    return 0

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

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

Solution (Python):
a, b = map(int, input().split())
a_, b_ = a % 4, b % 4
if a % 2:
    if a_ == b_:
        print(a)
    elif a_ == (b_-1) % 4:
        print(a^b)
    elif a_ == (b_-2) % 4:
        print(a^(b-1)^b)
    else:
        print(a^(b-2)^(b-1)^b)
else:
    if a_ == b_:
        print(b)
    elif a_ == (b_-1) % 4:
        print((b-1)^b)
    elif a_ == (b_-2) % 4:
        print((b-2)^(b-1)^b)
    else:
        print((b-3)^(b-2)^(b-1)^b)

Solution (Python):
A,B = map(int,input().split())
A-=1
def func(a):
    if a%2 == 1:
        onenum = a//2
        if onenum%2 == 1:
            return 0
        else:
            return 1
    else:
        onenum = a//2
        if onenum%2 == 0:
            return a
        else:
            return 1^a
print(func(B)^func(A))

Solution (Python):
n,m = map(int,input().split())
l = len(format(m,"b"))

sa = m-n
ans = 0
if sa % 2 ==  1:
    if sa % 4 != 3:
        ans += 1
else:
    if n % 2 == 0:
        if sa % 4 != 0:
            ans += 1
    else:
        if sa % 4 == 0:
            ans += 1
for i in range(1,l):
    count = 0
    x = m % 2**(i+1)
    y = n % 2**(i+1)
    if x < 2**i:
        count += 0
    else:
        count += x-2**i+1
    if y < 2**i:
        count += 2**i
    else:
        count += 2**(i+1)-y
    

    if count % 2 == 1:
        ans += 2**i
        
print(ans)

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

if A % 2 == 0 and B % 2 == 0:
    diff = (B - A + 1) // 2
    if diff % 2 == 1:
         print(1 ^ B)
    else :
        print(0 ^ B)
elif A % 2 == 0 and B % 2 == 1:
    diff = (B - A + 1) // 2
    if diff % 2 == 1:
        print(1)
    else :
        print(0)
elif A % 2 == 1 and B % 2 == 0:
    diff = (B - A) // 2
    if diff % 2 == 1:
        print(A ^ 1 ^ B)
    else :
        print(A ^ 0 ^ B)
else :
    diff = (B - A) // 2
    if diff % 2 == 1:
        print(A ^ 1)
    else :
        print(A ^ 0)

Solution (Python):
def f(a):
    b = a % 4
    if b == 0:
        return a
    elif b == 1:
        return (a-1) ^ (a)
    elif b == 2:
        return (a-2) ^ (a-1) ^ (a)
    return 0

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

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

Solution (Python):
def f(a):
    
    a+=1
    if a==0:
        return 0
    ans=0
    
    for i in range(44):
        
        
        
        loop = 1<<(i+1)
        cnt = (a//loop)*(loop//2)
        
        cnt+=max(0,(a%loop)-(loop//2))
        
        if cnt%2==1:
            ans+=(1<<i)
    return ans
a,b=map(int,input().split())
print(f(b)^f(a-1))

Solution (Python):
def f(N):
    if N==0:
        return 0
    if N==1:
        return 1
    if N==2:
        return 1^2
    if N==3:
        return 0
    k = 2
    while 2**k<=N:
        k += 1
    k -= 1
    if 2**k==N:
        return N
    n = (N-2**k)//4
    cnt = 0
    i = 2**k+4*n
    while i<=N:
        cnt = cnt^i
        i += 1
    return cnt
A,B = map(int,input().split())
if A==0 and B==0:
    print(0)
elif A==0 and B>0:
    print(f(B))
else:
    print(f(B)^f(A-1))

Solution (Python):
import sys
sys.setrecursionlimit(10**9)
INF=10**18
MOD=10**9+7
def input():
    return sys.stdin.readline().rstrip()

def main():
    A,B=map(int,input().split())
    B+=1
    ans=0
    N=max(len(bin(A)),len(bin(B)))-2
    for i in range(N):
        a=A//(2**(i+1))*(2**i)+max(A%(2**(i+1))-2**i,0)
        b=B//(2**(i+1))*(2**i)+max(B%(2**(i+1))-2**i,0)
        if (b-a)%2:
            ans|=(1<<i)
    print(ans)
    

if __name__ == '__main__':
    main()

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

def main():
    A, B = [int(x) for x in input().split()]
    a = [0] * 45
    if A == B:
        print(A)
        exit()
    for i in range(0, 44):
        x = (B // (2 ** i)) // 2 * (2 ** i)
        if (B // (2 ** i)) & 1:
            x += B % (2 ** i) + 1
        y = ((A - 1) // (2 ** i)) // 2 * (2 ** i)
        if ((A - 1) // (2 ** i)) & 1:
            y += (A - 1) % (2 ** i) + 1
        a[i] = x - y

    ans = 0
    for i, v in enumerate(a):
        if v & 1:
            ans += 2 ** i

    print(ans)

    
    

if __name__ == '__main__':
    main()

Solution (Python):

from math import log2,ceil
a,b=map(int,input().split())
if a==0 and b==0:
    print(0)
    exit()
if a==0:
    pass
elif a>=2:
    na=int(ceil(log2(a)))
nb=int(ceil(log2(b)))
l=[0]*(nb+1)

if a>=2:
    a-=1
    for i in range(na+1):
        q=a//(2**(i+1))
        r=a%(2**(i+1))
        r-=2**i
        if r<0:
            r=0
        elif r>=0:
            r+=1
        l[i]-=q*2**i+r

for i in range(nb+1):
    q=b//(2**(i+1))
    r=b%(2**(i+1))
    r-=2**i
    if r<0:
        r=0
    elif r>=0:
        r+=1
    l[i]+=q*2**i+r

for i in range(len(l)):
    l[i]=l[i]%2

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

Solution (Python):
A,B=[int(x) for x in str(input()).split()]

X=[]
m=len(bin(B)[2:])
temp=bin(A)[2:]
for i in range(m-len(temp)):
  temp="0"+temp
X.append(temp)
X.append(bin(B)[2:])


diff=B-A+1
t=diff%2
ans=""
for j in range(m-1):
  if t==0:
    if A%2==0:
      ans+="0"
    else:
      if X[0][j]==X[-1][j]:
        ans+="0"
      else:
        ans+="1"
  if t==1:
    if A%2==0:
      ans+=X[-1][j]
    else:
      ans+=X[0][j]

if diff%4==0:
  ans+="0"
elif diff%4==1:
  if A%2==0:
    ans+="0"
  else:
    ans+="1"
elif diff%4==2:
  ans+="1"
elif diff%4==3:
  if A%2==0:
    ans+="1"
  else:
    ans+="0"



print(int(ans,2))

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

def xor(n):
  if n%2 == 1:
    return (n//2 + 1)%2
  else:
    return xor(n-1) + n
  
print(xor(b)^xor(a-1))

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

def xor(n):
  if n%2 == 1:
    return (n//2 + 1)%2
  else:
    return xor(n-1) + n
  
print(xor(b)^xor(a-1))

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

def calc(x):
    if x%2 == 0:
        return (x//2%2)^x
    else:
        return (x+1)//2%2
print(calc(a-1)^calc(b))