You are given an array A of length N and an integer K.

   A function F(i,j) is defined below as, 
    F(i,j) = a_i ^ a_i+1 ^ a_i+2 ^... ^a_{j .}
   where a_i , a_i+1 , .. , a_j  are elements of array A and 0 <= i <= j < n .   

•    Symbol ^ is Exclusive Or. 

 You use the above function F(i,j) for each unique pair (i, j) , where 0 <= i < n and 0 <= j < n and i <= j ,  and put the results into a new  array B.

   Your task is to find the K_th largest element of array B.

   Note : Assume K is always valid and answer always exists for given K.

Input :

• The first line contains two numbers N and K .
• The second line contains N numbers - a₁,a₂,a₃,…,a_N .

Output :

• Output  the K_th largest element of array B .

Constraint :

• 1 <= N <= 10⁵
• 0 <= a_i <= 10⁶
• K >= 1 and  is always valid .