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

Solution (Python):
import sys

def S(): return sys.stdin.readline().rstrip()

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

def f(n):  
    res = 0
    while n % 4 != 3:
        res ^= n
        n -= 1
    return res

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

Solution (Python):
import sys

def S(): return sys.stdin.readline().rstrip()

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

def f(n):  
    res = 0
    for i in range(41):  
        if i == 0:
            res += ((n+1)//2) % 2
        else:
            a = n - ((n >> (i+1)) << (i+1))
            if a < 2**i or a % 2 == 1:
                continue
            else:
                res += 1 << i
    return res

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

Solution (Python):
def xor_sum(n):
    
    st =n -n%4
    n_list =[i for i in range(st,n+1)]
    ans =0
    for i in n_list:
        ans ^=i
    return ans


import sys
input = sys.stdin.readline
A,B = (int(i) for i in input().split())
ans =xor_sum(B) ^xor_sum(A-1)
print(ans)

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

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

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

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

Solution (Python):
def main():
    A, B = map(int, input().split())
    bin_B = bin(B)[2:]
    if A != 0:
        A -= 1
    bin_A = bin(A)[2:]
    cnt = [0] * len(bin_B)
    for i in range(len(bin_B)):
        loop = 2 ** (i+1)
        mod = B % loop
        if mod >= loop // 2:
            mod -= loop // 2
            mod += 1
        else:
            mod = 0
        cnt[i] = mod
        cnt[i] += (B // loop) * (loop // 2)
    for i in range(len(bin_A)):
        loop = 2 ** (i+1)
        mod = (A) % loop
        if mod >= loop // 2:
            mod -= loop // 2
            mod += 1
        else:
            mod = 0
        cnt[i] -= mod
        cnt[i] -= ((A) // loop) * (loop // 2)


    ans = 0
    for i in range(len(bin_B)):
        if cnt[i] % 2 == 1:
            ans += 2 ** i

    print(ans)


    



if __name__ == "__main__":
    main()

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

mid_xor = 0
if a%2 == 0 and b%2 == 1:
    even_cnt = (b-a+1)//2
    if even_cnt%2 == 0:
        mid_xor = 0
    else:
        mid_xor = 1
    print(mid_xor)

elif a%2 == 1 and b%2 == 0:
    even_cnt = (b-1-(a+1)+1)//2
    if even_cnt%2 == 0:
        mid_xor = 0
    else:
        mid_xor = 1
    print(a^mid_xor^b)

elif a%2 == 0 and b%2 == 0:
    even_cnt = (b-a)//2
    if even_cnt%2 == 0:
        mid_xor = 0
    else:
        mid_xor = 1
    print(mid_xor^b)
    
elif a%2 == 1 and b%2 == 1:
    even_cnt = (b-a)//2
    if even_cnt%2 == 0:
        mid_xor = 0
    else:
        mid_xor = 1
    print(a^mid_xor)

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

Solution (Python):
import math
import sys
sys.setrecursionlimit(10**9)

def mi(): return map(int,input().split())
def ii(): return int(input())
def isp(): return input().split()
def deb(text): print("-------\n{}\n-------".format(text))

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

    x_sum = 0
    ev_cnt = 0
    if A % 2 == 0:
        if B%2==0:
            x_sum ^=B
            ev_cnt = B//2-A//2 
        else:
            ev_cnt = math.ceil(B/2)-A//2 
             
    else:
        if B%2==0:
            x_sum ^=B
            x_sum ^= A
            ev_cnt = B//2-math.ceil(A/2)
        else:
            x_sum ^= A
            ev_cnt = math.ceil(B/2)-math.ceil(A/2)
    

    if ev_cnt % 2 == 0:
        print(x_sum)
    else:
        print(x_sum^1)

if __name__ == "__main__":
    main()

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

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

Solution (Python):
import sys

sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7


def resolve():
    a, b = map(int, input().split())

    def f(n):
        if n % 4 == 0:
            return n
        elif n % 4 == 1:
            return 1
        elif n % 4 == 2:
            return ((n // 4) + 1) * 4 - 1
        else:
            return 0

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


if __name__ == '__main__':
    resolve()

Solution (Python):

from math import log
A,B = map(int, input().split())

def f(x):
    if x <= 0:
        return []
    n = int(log(x,2))
    r = [0 for i in range(n+1)]
    while x > 0:
        n = int(log(x,2))
        for i in range(n):
            r[i] += pow(2,n-1)
        x -= pow(2,n)
        r[n] += x+1
    return r

a = f(A-1)
b = f(B)
for i,v in enumerate(a):
    b[i] -= v

ans = 0
for i,v in enumerate(b):
    if v % 2 == 1:
        ans += pow(2,i)
print(ans)

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





def xorall(aa):
    remz = aa % 4
    if remz == 0:
        return aa

    if remz == 1:
        return 1

    if remz == 2:
        return aa+1

    
    return 0

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

Solution (Python):
import sys
import heapq
import re
from itertools import permutations
from bisect import bisect_left, bisect_right
from collections import Counter, deque
from math import factorial, sqrt, ceil, gcd
from functools import lru_cache, reduce
from decimal import Decimal
INF = 1 << 60
MOD = 1000000007
sys.setrecursionlimit(10 ** 7)


class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


def dijkstra_heap(s, edge, n):
    
    d = [10**20] * n
    used = [True] * n 
    d[s] = 0
    used[s] = False
    edgelist = []
    for a,b in edge[s]:
        heapq.heappush(edgelist,a*(10**6)+b)
    while len(edgelist):
        minedge = heapq.heappop(edgelist)
        
        if not used[minedge%(10**6)]:
            continue
        v = minedge%(10**6)
        d[v] = minedge//(10**6)
        used[v] = False
        for e in edge[v]:
            if used[e[1]]:
                heapq.heappush(edgelist,(e[0]+d[v])*(10**6)+e[1])
    return d


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 lcm(x, y):
    return (x * y) // gcd(x, y)


def lcm_list(numbers):
    return reduce(lcm, numbers, 1)


def gcd_list(numbers):
    return reduce(gcd, numbers)


def is_prime(n):
    if n <= 1:
        return False
    p = 2
    while True:
        if p ** 2 > n:
            break
        if n % p == 0:
            return False
        p += 1
    return True



def eratosthenes(limit):
    A = [i for i in range(2, limit+1)]
    P = []

    while True:
        prime = min(A)
        
        if prime > sqrt(limit):
            break
            
        P.append(prime)
            
        i = 0
        while i < len(A):
            if A[i] % prime == 0:
                A.pop(i)
                continue
            i += 1
            
    for a in A:
        P.append(a)
            
    return P


def permutation_with_duplicates(L):

    if L == []:
        return [[]]

    else:
        ret = []

        
        S = sorted(set(L))

        for i in S:

            data = L[:]
            data.remove(i)

            for j in permutation_with_duplicates(data):
                ret.append([i] + j)

        return ret

def make_divisors(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]


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

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


def f(first, last):
    diff = last - first
    m = diff % 4
    res = 0
    
    if first % 2 == 0:
        for i in reversed(range(last - m, last + 1)):
            res ^= i
        return res
    else:
        for i in reversed(range(last - m + 1, last + 1)):
            res ^= i
        res ^= first
        return res


print(f(A, B))

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

def xorsum(x):
  if x % 4 == 1:
    return 1
  elif x % 4 == 3:
    return 0
  elif x % 4 == 0:
    return 1 ^ (x+1)
  else:
    return 0 ^ (x+1)

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

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

def xorsum(x):
  if x % 4 == 1:
    return 1
  elif x % 4 == 3:
    return 0
  elif x % 4 == 0:
    return x
  else:
    return 1 ^ x

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

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

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

c = sum_xor(b)
d = sum_xor(a-1)
print(c^d)

Solution (Python):
a,b = map(int,input().split())
am = a%4
bm = b%4
ad = a//4
bd = b//4
ans = 0
if ad == bd:
    for i in range(a, b+1):
        ans ^= i
else:
    while am != 0:
        ans ^= a
        a += 1
        am += 1
        am %= 4
    while bm != 3:
        ans ^= b
        b -= 1
        bm -= 1
        bm %= 4
print(ans)

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

def F(n):
    a = n//2
    if n % 2 == 0:
        if a % 2 == 0:
            return n
        else:
            return n ^ 1
    else:
        if a % 2 == 0:
            return 1
        else:
            return 0

ans = F(a-1) ^ F(b)
print(ans)

Solution (Python):
import sys
sys.setrecursionlimit(10**9)

def mi(): return map(int,input().split())
def lmi(): return list(map(int,input().split()))
def ii(): return int(input())
def isp(): return input().split()


a,b=mi()

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

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

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


def F(n):
    a = n//2
    if n % 2 == 0:
        if a % 2 == 0:
            return n
        else:
            return n ^ 1
    else:
        if a % 2 == 0:
            return 1
        else:
            return 0


ans = F(a-1) ^ F(b)
print(ans)

Solution (Python):
[A,B] = list(map(int,input().split()))
X = B-A

if A%2 == 0:
    if X%4 ==1:
        out=1
    elif X%4 ==2:
        out=1^B
    elif X%4 ==3:
        out=0
    else:
        out=B

else:
    if X%4 ==1:
        out=A^B
    elif X%4 ==2:
        out=A^1
    elif X%4 ==3:
        out=A^B^1
    else:
        out=A

print(out)

Solution (Python):
import sys
import time




import math
start=time.time()
input = sys.stdin.readline
sys.setrecursionlimit(10**8)
inf = 10**18
MOD = 1000000007
ri = lambda : int(input())
rs = lambda : input().strip()
rl = lambda : list(map(int, input().split()))
a,b = rl()
c=a%4
d=b%4
ans=0
for i in range(4-c):
    ans^=a+i
for i in range(d+1):
    ans^=b-i
print(ans)

Solution (Python):
import sys
import time




import math
start=time.time()
input = sys.stdin.readline
sys.setrecursionlimit(10**8)
inf = 10**18
MOD = 1000000007
ri = lambda : int(input())
rs = lambda : input().strip()
rl = lambda : list(map(int, input().split()))
a,b = rl()
c=a%4
d=b%4
ans=0
for i in range(4-c):
    ans^=a+i
for i in range(d+1):
    ans^=b-i
print(ans)

Solution (Python):
A,B = list(map(int,input().split()))
X = B-A
if A%2==0:
    if X%4==0:
        out = B
    if X%4==1:
        out = 1
    if X%4==2:
        out = B^1
    if X%4==3:
        out = 0
else:
    if X%4==0:
        out = A
    if X%4==1:
        out = A^B
    if X%4==2:
        out = A^1
    if X%4==3:
        out = A^B^1
print(out)

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

res = 0
i = 0
two = 2
while 1 << i <= b:
    mod_a, mod_b = a % two, b % two
    tmp_a, tmp_b = a - mod_a + two, b - mod_b

    cnt = ((tmp_b - tmp_a) // two) * (two // 2)
    cnt += min(two - mod_a, two // 2)
    cnt += max(mod_b - two // 2 + 1, 0)
    
    if cnt % 2 == 1:
        res += two // 2
    
    two *= 2
    i += 1

print(res)

Solution (Python):
A, B = map(int, input().split())
if A == B:
    print(A)
else:
    K = []
    if A % 2 == 1:
        K.append(A)
        A += 1
    if (B - A) % 2 == 0:
        if ((B - A) // 2) % 2 == 0:
            K.append(B)
        else:
            K.append(1)
            K.append(B)
    else:
        if ((B - A - 1) // 2) % 2 == 0:
            K.append(B-1)
            K.append(B)
        else:
            K.append(1)
            K.append(B-1)
            K.append(B)
    ans = 0
    for i in K:
        ans = (ans ^ i)
    print(ans)

Solution (Python):
A,B = map(int,input().split())
if A==0:
    fa = 0
else:
    v = (A-1)%4
    fa = 1 if v==2 or v ==1 else 0
    fa = fa ^ (A-1) if v%2==0 else fa
if B==0:
    fb = 0
else:
    v = (B)%4
    fb = 1 if v==2 or v ==1 else 0
    fb = fb ^ B if v%2==0 else fb
print(fa ^ fb)

Solution (Python):

def solve(x):
    if x % 4 == 3:
        return 0
    elif x % 4 == 0:
        return x
    elif x % 4 == 1:
        return x ^ (x - 1)
    elif x % 4 == 2:
        return x ^ (x - 1) ^ (x - 2)


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


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

Solution (Python):
a,b=map(int,input().split())
A,B=a%2>0,b%2<1
print(a*A^((b-B-(a-1^A))//2%2)^b*B)

Solution (Python):
import sys
import itertools

import time
import math
 
sys.setrecursionlimit(10 ** 7)
 
from collections import defaultdict
 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

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

first = A
last = B
left = 0
if A % 2 == 1:
    first += 1
    left ^= A
if B % 2 == 0:
    last -= 1
    left ^= B

if ((last - first) // 2 + 1) % 2 == 0:
    print(left)
else:
    print(1 ^ left)

Solution (Python):
import sys


def input():
    return sys.stdin.readline().strip()


sys.setrecursionlimit(20000000)

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


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


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

    print(answer)


if __name__ == "__main__":
    main()

Solution (Python):
a, b = map(int, input().split())
def f(x):
    return 0 if x <= 0 else x >> 1 & 1 ^ 1 if x & 1 else f(x - 1) | x
print(f(b) ^ f(max(0, a - 1)))

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

def f(a):
    if a <= 200:
        rv = 0
        for i in range(a + 1):
            rv ^= i
        return rv
    d = 1
    while d <= a:
        d <<= 1
    d >>= 1
    return (0 if a & 1 else d) | f(a - d)

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

Solution (Python):
def xorsum(n):
    if n % 2:
        return 0 if (n // 2) % 2 else 1
    else:
        return n + 1 if (n // 2) % 2 else n

a, b = map(int, input().split())
if a != 0:
    print(xorsum(b) ^ xorsum(a - 1))
else:
    print(xorsum(b))

Solution (Python):
import sys
from collections import defaultdict

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline

in_n = lambda: int(readline())
in_nn = lambda: map(int, readline().split())
in_s = lambda: readline().rstrip().decode('utf-8')


def main():

    
    A, B = in_nn()
    d = defaultdict(lambda: 0)

    n = 1
    while n <= A:
        n *= 2
        r = A % n
        
        if r >= n // 2:
            d[n] = (r - n // 2) % 2

    n = 1
    while n <= B:
        n *= 2
        r = B % n
        
        if r >= n // 2:
            d[n] ^= (r - n // 2 + 1) % 2

    n = 2
    ans = 0
    while n <= max(A, B):
        n *= 2
        ans += (n // 2) * d[n]

    d = (B - A + 1) % 4
    if A % 2 == 0:
        if d == 2 or d == 3:
            ans += 1
    if A % 2 == 1:
        if d == 1 or d == 2:
            ans += 1

    print(ans)


if __name__ == '__main__':
    main()

Solution (Python):
def main():
    a, b = list(map(int, input().split()))
    if b - a <= 3:
        ans = a
        for i in range(a + 1, b + 1):
            ans = ans ^ i
        print(ans)
    else:
        if a % 4 == 0:
            ans = 0
        elif a % 4 == 1:
            ans = a ^ (a + 1) ^ (a + 2)
        elif a % 4 == 2:
            ans = a ^ (a + 1)
        else:
            ans = a
        if b % 4 == 0:
            ans = ans ^ b
        elif b % 4 == 1:
            ans = ans ^ (b - 1) ^ b
        elif b % 4 == 2:
            ans = ans ^ (b - 2) ^ (b - 1) ^ b
        else:
            ans = ans ^ (b - 3) ^ (b - 2) ^ (b - 1) ^ b
        print(ans)



if __name__ == '__main__':
    main()

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

Solution (Python):
a,b=map(int,input().split())
f=lambda x:-(-x//2)%2^x*(x%2^1)
print(f(a-1)^f(b))

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

if a & 1 == 0 and (b-a+1)%2==0:
    ans = ((b-a+1)//2)%2
elif a & 1 == 0 and (b-a+1)%2==1:
    ans = ((b-a+1)//2)%2 ^ b
elif a & 1 == 1 and (b-a)%2==0:
    ans = ((b-a)//2)%2 ^ a
else:
    ans = ((b-a)//2)%2 ^ a ^ b
print(ans)

Solution (Python):
a,b=map(int,input().split())
def f(x):
  r=x%2^x//2%2
  p=2
  for i in range(len(bin(x))-3):
    r+=p-p*(x%2 or x%(p*2)<p)
    p*=2
  return r
print(f(a-1)^f(b))

Solution (Python):
a,b=map(int,input().split())
def xor_sum(x):
  r=x%2^x//2%2
  p=2
  for i in range(len(bin(x))-3):
    r+=p*(x%2<1 and x%(p*2)>=p)
    p*=2
  return r
print(xor_sum(a-1)^xor_sum(b))

Solution (Python):



import sys
readline = sys.stdin.readline

A,B = map(int,readline().split())
a = 0
for i in range(((A - 1) // 4) * 4,A):
  a ^= i
  
b = 0
for i in range((B // 4) * 4,B + 1):
  b ^= i

print(a ^ b)

Solution (Python):
A,B = map(int,input().split())
A = A-1
a = A % 2 
b = B % 2

if a == 1:
  A = (A+1)//2%2
else:
  A += (A//2)%2
if b == 1:
  B = (B+1)//2%2
else:
  B += (B//2)%2

ans = [0 for i in range(100)]

bin_a = format(A, 'b')
bin_b = format(B, 'b')

for i in range(len(bin_a)):
  ans[len(bin_a)-i-1] += int( bin_a[i] )
for i in range(len(bin_b)):
  ans[len(bin_b)-i-1] += int( bin_b[i] )
for i in range(100):
  ans[i] = ans[i]%2

a=0
for i in range(100):
  a += ans[i] * (2**i)
print(int(a))

Solution (Python):

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


def xor_0_to_N(N):
    if (N+1) % 2 == 0:
        s = (N+1) // 2 % 2
    else:
        s = ((N+1) // 2 % 2) ^ N
    return s

"""
XOR = 0
for i in range(1, 20):
    print("idx", i)
    XOR ^= i
    print(XOR)
    print(xor_0_to_N(i))
"""

print(xor_0_to_N(A-1) ^ xor_0_to_N(B))

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


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


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

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


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


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

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

if __name__ == '__main__':
    main()

Solution (Python):
def resolve():
    A, B = list(map(int, input().split()))
    ans = A
    i = A + 1
    warped = False
    while i <= B:
        if not warped and i % 4 == 0:
            i = B - B%4
            warped = True
        else:
            ans = ans ^ i
            i += 1
    print(ans)

if '__main__' == __name__:
    resolve()

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

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

def f(n):
    if n%4==3:
        return 0
    elif n%4==2:
        return n^1
    elif n%4==1:
        return 1
    else:
        return n

if __name__=="__main__":
    main()

Solution (Python):
def xor(n):
    if n == 0: return 0
    x = 0
    if ((n + 1) // 2) % 2 != 0: x = 1
    if n % 2 == 0: x ^= n
    return x

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

Solution (Python):
def get_one_cnts(n):
    one_cnts_dic = []
    for i in range(0,40): 
        if i == 0:
            if n%4 in [1,2]:
                one_cnts_dic.append(1)
            else:
                one_cnts_dic.append(0)
        else:
            cycle = 2**(i+1) 
            if n%cycle in range(cycle//2, cycle, 2):
                one_cnts_dic.append(1)
            else:
                one_cnts_dic.append(0)
    return one_cnts_dic

a,b = map(int, input().split())
a_one_cnts = get_one_cnts(a-1)
b_one_cnts = get_one_cnts(b)


ans = 0
for i in range(40):
    if a_one_cnts[i] ^ b_one_cnts[i]:
        ans += 2**i

print(ans)

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

ans = 0


for i in range(1, 41):
    m = 2 ** (i-1)
    n = 2 * m
    a = (A // n) * m + max(0, A % n - m)
    b = ((B+1) // n) * m + max(0, (B+1) % n - m)

    if (b-a) % 2 == 1:
        ans += m

print(ans)

Solution (Python):






from collections import deque



a,b=map(int,input().split())
if a==b:
  print(a)
  exit()
if a==0:
  i=0
  resb=0
  while True:
    if i==0:
      if ((b+1)//2)%2==1:
        resb+=1
      i+=1
      continue
    if 2**i>b+1:
        break
    if ((b+1)%(2**i))%2==1 and ((b+1)//(2**i))%2==1:
        resb+=2**i
    i+=1
  print(resb)
  exit()
  
n_b=b.bit_length()
n_a=(a-1).bit_length()
i=0
res=0

while True:
    if i==0:
      if (a//2)%2==1:
        res+=1
      i+=1
      continue
    if 2**i>a:
        break
    if (a%(2**i))%2==1 and (a//(2**i))%2==1:
        res+=2**i
    i+=1
i=0
resb=0
while True:
  if i==0:
    if ((b+1)//2)%2==1:
      resb+=1
    i+=1
    continue
  if 2**i>b+1:
        break
  if ((b+1)%(2**i))%2==1 and ((b+1)//(2**i))%2==1:
        resb+=2**i
  i+=1
print(res^resb)

Solution (Python):
def f(x):
    cou = 0
    re = 0
    while True:
        if x < 2**cou:
            break
        if cou == 0:
            if 1 <= x % 4 <= 2:
                re += 1
        else:
            p = x % (2**(cou+1))
            if 2**cou <= p and p % 2 == 0:
                re += 2**cou
        cou += 1
    return re
a , b = map(int,input().split())

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

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


def F(x):
    res = 0
    p, q = divmod(x+1, 2)
    if q:
        res ^= x
    if p % 2:
        res ^= 1
    return res
  

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

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


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

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

n = b - a + 1


if n % 2 == 0:
  if a % 2 == 1:
    ans = a ^ (((n - 2) // 2) % 2) ^ b
  else:
    m = n // 2
    ans = (m + 1) % 2 ^ 1
else:
  nn = (n - 1) // 2
  if a % 2 == 1:
    ans = (nn % 2) ^ a
  else:
    ans = (nn % 2) ^ b
    
print(ans)

Solution (Python):
A, B = map(int,input().split(' '))
B += 1
l = "1" if A%4 in [0,1] else "0"
r = "1" if B%4 in [0,1] else "0"
n = 2
while n <= A:
    if A%(2*n)-n <= 0 or A%(2*n)%2 == 0:
        l += "0"
    else:
        l += "1"
    n *= 2
n = 2
while n <= B:
    if B%(2*n)-n <= 0 or B%(2*n)%2 == 0:
        r += "0"
    else:
        r += "1"
    n *= 2
print(int(l[::-1], 2)^int(r[::-1], 2))

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

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

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

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

Solution (Python):
a,b = map(int,input().split())
if a==0:
    print(b)
    exit()
ab = bin(a-1)[2:]
bb = bin(b)[2:]


sa = []
sb = []
if int(bb[-1]):
    sb = [1]
else:
    for i in bb:
        sb += [int(i)]
if a>0:
    if int(ab[-1]):
        sa = [1]
    else:
        for i in ab:
            
            sa += [int(i)]
sa[-1] = (a//2)%2
sb[-1] = ((b+1)//2)%2



ta = "".join([str(i) for i in sa])
tb = "".join([str(i) for i in sb])
ta = int(ta,2)
tb = int(tb,2)


ans = ta^tb


print(ans)

Solution (Python):

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

A -= 1

if (A+1) % 2 == 0:
    a = (A+1) // 2 % 2
else:
    a = (A // 2 % 2) ^ A

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

print(a ^ b)

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



def solve(n, i):
    res = 0
    mod = 2**i
    c = n // mod
    res += c*mod//2
    if n % mod >= mod//2:
        res += (n%mod - mod//2 + 1)
    return res

b_list = [0]*40
a_list = [0]*40
ans = 0
for i in range(1, 41):
    num_l = solve(b, i)
    num_r = solve(a-1, i)
    num_one = num_l - num_r
    if num_one% 2 == 1:
        ans += 2**(i-1)
print(ans)

Solution (Python):


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

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

list_ = []
ans = 0
if a % 2 != 0:
    list_.append(a)
    a += 1

if b % 2 == 0:
    list_.append(b)
    b -= 1

num = ((b+1)-a)//2
if num % 2 == 0:
    ans = 0
else:
    ans = 1


for i in list_:
    ans = ans ^ i
print(ans)

Solution (Python):
def main():
    a, b = map(int, input().split())
    c = [[(b - a) // 2 % 2 ^ b, (b - a + 1) // 2 % 2], [a ^ b ^ (b - a - 1) // 2 % 2, (b - a + 1) // 2 % 2 ^ a]]
    i, j = a % 2, b % 2
    print(c[i][j])


if __name__ == '__main__':
    main()

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())
xorA = [0] * 41
xorB = [0] * 41
def xor_list(l, N):
    k = 1
    while 2 ** k // 2 <= N:
        tmp = (N+1) % (2 ** k)
        if k == 1:
            l[k-1] = (N+1) // (2 ** k)
            k += 1
        elif tmp <= 2 ** k // 2:
            k += 1
            continue
        else:
            l[k-1] = (tmp - 2 ** k // 2) % 2
            k += 1
        if k == 1:
            count = (N + 1) // (2 ** k) + tmp + 1
            l[0] = (count % 2)
xor_list(xorA, A-1)
xor_list(xorB, B)
ans = 0
for i in range(41):
    ans += abs(xorA[i] - xorB[i]) % 2 * (2 ** i)
print(ans)

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

if a%2==0:
  if b%2==0:
    c=((b-1)//2-a//2+1)%2
    if c==0:
      print(b)
    else:
      if b%2==0:
        print(b+1)
      else:
        print(b-1)
  else:
    print((b//2-a//2+1)%2)
else:
  if b%2==0:
    c=(b//2-a//2-1)%2
    ans=list(format(b,"b")[::-1])
    ans[0]=str((int(ans[0])+c)%2)
    for i,x in enumerate(format(a,"b")[::-1]):
      ans[i]=str((int(ans[i])+int(x))%2)

    ans=str("0b"+"".join(ans[::-1]))
    print(int(ans,0))
    
  else:
    c=(b//2-(a+1)//2+1)%2
    if c==0:
      print(a)
    else:
      if a%2==0:
        print(a+1)
      else:
        print(a-1)

Solution (Python):
import numpy as np
from collections import deque
from collections import defaultdict
import heapq
import collections
import itertools
import bisect


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













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


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

Solution (Python):
def main():
    a,b = map(int, input().split())
    n = (b-a+1)
    k = n//2

    if n%2==0:
        if a%2==0:
            if k%2==0:
                res = 0
            else:
                res =1
        else:
            k = (n-2)//2
            if k%2 == 1:
                res=(a^b^1)
            else:
                res = a^b
    else:
        if a%2 == 0:
            if k%2 == 0:
                res = (b)
            else:
                res = b^1
        else:
            if k%2==1:
                res = a^1
            else:
                res = a
    print(res)





if __name__ == '__main__':
    main()

Solution (Python):
a, b = map(int, input().split())
def calc(x):
    rtn = 0
    i = 1
    while i<=x:
        i *= 2
        if i==2:
            if x%4==1 or x%4==2:
                rtn += 1
            continue
        if x%i<i//2:
            continue
        rtn += ((x%i-i//2+1)%2)*(i//2)
    return rtn
if a==0:
    print(calc(b))
else:
    print(calc(a-1)^calc(b))