Problem: Mahmoud and Ehab are on the third stage of their adventures now. As you know, Dr. Evil likes sets. This time he won't show them any set from his large collection, but will ask them to create a new set to replenish his beautiful collection of sets.

Dr. Evil has his favorite evil integer x. He asks Mahmoud and Ehab to find a set of n distinct non-negative integers such the bitwise-xor sum of the integers in it is exactly x. Dr. Evil doesn't like big numbers, so any number in the set shouldn't be greater than 106.

Input

The only line contains two integers n and x (1 ≤ n ≤ 105, 0 ≤ x ≤ 105) — the number of elements in the set and the desired bitwise-xor, respectively.

Output

If there is no such set, print "NO" (without quotes).

Otherwise, on the first line print "YES" (without quotes) and on the second line print n distinct integers, denoting the elements in the set is any order. If there are multiple solutions you can print any of them.

Examples

Input

5 5


Output

YES
1 2 4 5 7

Input

3 6


Output

YES
1 2 5

Note

You can read more about the bitwise-xor operation here: <https://en.wikipedia.org/wiki/Bitwise_operation#XOR>

For the first sample <image>.

For the second sample <image>.

Solution (in PYTHON3):

Solution:
# cook your dish here
from collections import defaultdict,OrderedDict,Counter
from sys import stdin,stdout
from bisect import bisect_left,bisect_right
# import numpy as np
from queue import Queue,PriorityQueue
from heapq import *
from statistics import *
from math import *
import fractions
import copy
from copy import deepcopy
import sys
import io
sys.setrecursionlimit(10000)
import math
import os
import bisect
import collections
mod=pow(10,9)+7
import random
from random import *
from time import  time;
def ncr(n, r, p=mod):
    num = den = 1
    for i in range(r):
        num = (num * (n - i)) % p
        den = (den * (i + 1)) % p
    return (num * pow(den,
            p - 2, p)) % p
def normalncr(n,r):
    r=min(r,n-r)
    count=1;
    for i in range(n-r,n+1):
        count*=i;

    for i in range(1,r+1):
        count//=i;
    return count

inf=float("inf")
adj=defaultdict(set)
visited=defaultdict(int)
def addedge(a,b):
    adj[a].add(b)
    adj[b].add(a)
def bfs(v):
    q=Queue()
    q.put(v)
    visited[v]=1
    while q.qsize()>0:
        s=q.get_nowait()
        print(s)
        for i in adj[s]:
            if visited[i]==0:
                q.put(i)
                visited[i]=1
def dfs(v,visited):
    if visited[v]==1:
        return;
    visited[v]=1

    print(v)
    for i in adj[v]:
        dfs(i,visited)
# a9=pow(10,6)+10
# prime = [True for i in range(a9 + 1)]
# def SieveOfEratosthenes(n):
#     p = 2
#     while (p * p <= n):
#         if (prime[p] == True):
#             for i in range(p * p, n + 1, p):
#                 prime[i] = False
#         p += 1
# SieveOfEratosthenes(a9)
# prime_number=[]
# for i in range(2,a9):
#     if prime[i]:
#         prime_number.append(i)
def reverse_bisect_right(a, x, lo=0, hi=None):
    if lo < 0:
        raise ValueError('lo must be non-negative')
    if hi is None:
        hi = len(a)
    while lo < hi:
        mid = (lo+hi)//2
        if x > a[mid]:
            hi = mid
        else:
            lo = mid+1
    return lo
def reverse_bisect_left(a, x, lo=0, hi=None):
    if lo < 0:
        raise ValueError('lo must be non-negative')
    if hi is None:
        hi = len(a)
    while lo < hi:
        mid = (lo+hi)//2
        if x >= a[mid]:
            hi = mid
        else:
            lo = mid+1
    return lo

def get_list():
    return list(map(int,input().split()))
def get_str_list_in_int():
    return [int(i) for i in list(input())]
def get_str_list():
    return list(input())
def get_map():
    return map(int,input().split())
def input_int():
    return int(input())
def matrix(a,b):
    return [[0 for i in range(b)] for j in range(a)]
def swap(a,b):
    return b,a
def find_gcd(l):
    a=l[0]
    for i in range(len(l)):
        a=gcd(a,l[i])
    return a;
def is_prime(n):
    sqrta=int(sqrt(n))
    for i in range(2,sqrta+1):
        if n%i==0:
            return 0;
    return 1;
def prime_factors(n):
    while n % 2 == 0:
        return [2]+prime_factors(n//2)
    sqrta = int(sqrt(n))


    for i in range(3,sqrta+1,2):
        if n%i==0:
            return [i]+prime_factors(n//i)

    return [n]
def p(a):
    if type(a)==str:
        print(a+"\n")
    else:
        print(str(a)+"\n")
def ps(a):
    if type(a)==str:
        print(a)
    else:
        print(str(a))
def kth_no_not_div_by_n(n,k):
    return k+(k-1)//(n-1)
def forward_array(l):
    n=len(l)
    stack = []
    forward=[0]*n
    for i in range(len(l) - 1, -1, -1):
        while len(stack) and l[stack[-1]] < l[i]:
            stack.pop()
        if len(stack) == 0:
            forward[i] = len(l);
        else:
            forward[i] = stack[-1]
        stack.append(i)
    return forward;
def backward_array(l):
    n=len(l)
    stack = []
    backward=[0]*n
    for i in range(len(l)):
        while len(stack) and l[stack[-1]] < l[i]:
            stack.pop()
        if len(stack) == 0:
            backward[i] = -1;
        else:
            backward[i] = stack[-1]
        stack.append(i)
    return backward
nc="NO"
yc="YES"
ns="No"
ys="Yes"

# import math as mt
# MAXN=10**7
# spf = [0 for i in range(MAXN)]
# def sieve():
#     spf[1] = 1
#     for i in range(2, MAXN):
#         # marking smallest prime factor
#         # for every number to be itself.
#         spf[i] = i
#
#         # separately marking spf for
#     # every even number as 2
#     for i in range(4, MAXN, 2):
#         spf[i] = 2
#
#     for i in range(3, mt.ceil(mt.sqrt(MAXN))):
#
#         # checking if i is prime
#         if (spf[i] == i):
#
#             # marking SPF for all numbers
#             # divisible by i
#             for j in range(i * i, MAXN, i):
#
#                 # marking spf[j] if it is
#                 # not previously marked
#                 if (spf[j] == j):
#                     spf[j] = i
# def getFactorization(x):
#     ret = list()
#     while (x != 1):
#         ret.append(spf[x])
#         x = x // spf[x]
#
#     return ret
# sieve()






# input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
# input=stdin.readline
# print=stdout.write

def rem_list(rem):
    l=[]
    for i in range(10**6-1,10**6-rem-1,-1):
        l.append(i)
    return l;

def lista(n,x,rem):
    if x==0:
        if n%4==2:
            rem-=4
            l = rem_list(rem)
            m=[x+2**17,2**17+1,2**17+2,2**17+4,2**17+8,2**17+15]
            print(*(l+m))
            # xor(l+m)
            return None
    if n==1:
        return [x];
    elif n==2:
        return [x+2**17,2**17]
    elif n==3:
        return [x+2**17,2**18,2**17+2**18]
    elif n==4:
        return [x,2**17,2**18,2**17+2**18]
def xor(a):
    xora=0
    for i in a:
        xora^=i;
    print(xora)
t=1
for i in range(t):
    n,x=get_list()
    if x==0:
        if n==2:
            print(nc)
            continue



    rem=n//4;
    n-=rem*4;
    if n==0:
        n=4;
        rem-=1
    rem*=4
    print(yc)
    l=rem_list(rem)
    m=lista(n,x,rem)
    if m!=None:
        print(*(l+m))
    # xor(l+m)