Josh has a wall of colour $X$. However, last night, people graffitied the entire wall! Josh now needs to obtain a large amount of paint of colour $X$ so that he can repaint the wall, covering up the modern art.

In his storeroom, Josh finds $N$ buckets of paint. The $i$-th bucket has paint of colour $a_i$. Josh can repeatedly perform the following operation:

• First, select one bucket of paint.
• Then, evenly divide the paint in this bucket amongst the remaining buckets. The chosen bucket is then discarded.
• If paint of colour $X$ was poured into a bucket of paint of colour $Y$, then the bucket will now contain paint of colour $X\oplus Y$, due to the mysterious chemical properties of the paint.

Here, $\oplus$ denotes the bitwise XOR operator.

Can you help Josh determine whether he can end up with exactly one bucket, with this bucket containing paint of colour $X$?

Constraints

$2\le N\le {10}^6$

$0\le X,a_i<2^{30}$

Subtask 1 [20%]

$2\le N\le 9$

Subtask 2 [50%]

$2\le N\le 2000$

Subtask 3 [30%]

No additional constraints.

Input Specification

The first line contains two space-separated integers, $N$ and $X$.

The second line contains $N$ space-separated integers, $a_1,a_2,\dots ,a_N$.

Output Specification

On a single line, output YES if Josh can end up with a single bucket containing paint of colour $X$, and NO otherwise.

Sample Input 1

3 1
1 2 3

Sample Output 1

YES

Explanation for Sample Output 1

Initially, there are three buckets, containing paint of colours $1$, $2$ and $3$ respectively. Even though Josh already has paint of colour $1$, he wants a single bucket of colour $X$, with no other buckets.

First, Josh can pour the paint in bucket $1$ into the other two buckets. The bucket which initially contained paint of colour $2$ now contains paint of colour $1\oplus 2=3$. The bucket which initially contained paint of colour $3$ now contains paint of colour $1\oplus 3=2$.

At this point, Josh has two buckets, containing paint of colours $3$ and $2$ respectively. If he pours the paint in the first bucket into the second bucket, he will end up with a single bucket containing paint of colour $3\oplus 2=1$.

Sample Input 2

3 4
1 2 3

Sample Output 2

NO