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Time Limit: 1.0 s

Memory Limit: 256.0 MB

Description

Both Hridoy and Roy enjoy solving mathematical puzzles as well as they are very close friends. They like challenging one another constantly, in keeping with this pattern, Hirdoy gave Roy a bitwise XOR problem which is very interesting for the bit lover. Hridoy set an array of N integers (\(A_1\), \(A_2\),... +\(A_N\)) together with an integer value (K). Roy was allowed to select a number X within this range which is 0 ≤ X ≤ K, By Choosing this X, Roy had to determine the maximum value of F(X) = (\(A_1\) ⊕ X) + (\(A_2\) ⊕ X) +... + (\(A_N\) ⊕ X).

Roy is asking for your assistance in fixing this problem since he is finding it tough to do so because of his busy schedule.
NOTE: ⊕ means XOR where XOR is a bitwise operator, and it stands for "exclusive or." It performs logical operation. If input bits are the same, then the output will be false(0) else true(1)

Input

The first line contains two integers N (3 ≤ N ≤ \(10^5\)) and K (1 ≤ K ≤ \(10^{12}\))
The second line contais N integers \(A_1\) , \(A_2\) ,,, \(A_N\) (1 ≤ \(A_N\) ≤ \(10 ^ {12}\))

Output

Print the maximum Value of F

Sample

3 7
1 6 3

14