CF862C.Mahmoud and Ehab and the xor

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.

马哈茂德和埃哈布现在正处于他们冒险的第三阶段。众所周知，邪恶博士喜欢集合。这一次，他不会向他们展示自己庞大集合收藏中的任何集合，而是要求他们创建一个新集合，以充实他那精美的集合收藏。

邪恶博士有他最钟爱的“邪恶整数”$x$。他要求马哈茂德和埃哈布找出一个由 $n$ 个互不相同的非负整数组成的集合，使得该集合中所有整数的按位异或（bitwise-xor）和恰好等于 $x$。邪恶博士不喜欢大数，因此集合中的任意数都不应超过 $10^6$。

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.

唯一一行包含两个整数 $n$ 和 $x$（$1 ≤ n ≤ 10^5$，$0 ≤ x ≤ 10^5$）——分别表示集合中元素的个数和目标按位异或值。

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.

如果不存在这样的集合，输出 "NO"（不带引号）。

否则，第一行输出 "YES"（不带引号），第二行输出 n 个互不相同的整数，以任意顺序表示该集合中的元素。如果存在多种解，输出任意一种即可。

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

For the first sample .

For the second sample .

你可以在这里了解更多关于按位异或（bitwise-xor）运算的信息：https://en.wikipedia.org/wiki/Bitwise_operation#XOR

对于第一个样例：。

对于第二个样例：。