In meteorology, a cyclone is a large scale air mass that rotates around a strong center of low atmospheric pressure. Cyclones have also been seen on extraterrestrial planets, such as Mars and Neptune. On one of such planets outside our solar system, there is a strange cyclonic system. The strength K of an oceanic cyclone is always equal to the XOR sum of the area of neighboring islands.

You are given a number N denoting total number of islands. You have to print number of subsets such that the XOR sum of the area of islands is equal to strength of cyclone i.e K.

Note :

a) Two subsets (A and B) are considered different if atleast one number in subset A is from different index than in subset B .

b) Xor sum is XOR (^) of all the numbers in subset.

c) XOR sum of empty subset is zero.

Input :
First line of input is two integers N and K representing number of islands and strength of cyclone.
Next line contains N integers representing the area of islands.

Output :
Output total number of subsets whose XOR sum is K.

Constraints:

$1 \le A_{i} \le 10^{18}$

$1 \le N \le 40$

1 <= k <= 10¹⁸