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